Fractional thoughts (Q5236846)

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scientific article; zbMATH DE number 7117898

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English	Fractional thoughts	scientific article; zbMATH DE number 7117898

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scholarly article

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Fractional thoughts (English)

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Nicola Garofalo

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New Developments in the Analysis of Nonlocal Operators

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publication date

16 October 2019

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full work available at URL

https://arxiv.org/abs/1712.03347

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MaRDI profile type

MaRDI publication profile

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Large \(s\)-harmonic functions and boundary blow-up solutions for the fractional Laplacian

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Very large solutions for the fractional Laplacian: towards a fractional Keller-Osserman condition

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Getting acquainted with the fractional Laplacian

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Optimal results for the fractional heat equation involving the Hardy potential

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Improvement of Besov regularity for solutions of the fractional Laplacian

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Uniqueness and related analytic properties for the Benjamin-Ono equation -- A nonlinear Neumann problem in the plane

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A Nonlocal<i>p</i>-Laplacian Evolution Equation with Nonhomogeneous Dirichlet Boundary Conditions

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Optimal regularity of lower dimensional obstacle problems

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The structure of the free boundary for lower dimensional obstacle problems

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Riesz transform on manifolds and heat kernel regularity

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Analysis and Geometry of Markov Diffusion Operators

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Fractional powers of closed operators and the semigroups generated by them

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Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations

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Some constructions for the fractional Laplacian on noncompact manifolds

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Sur une classe d'opérateurs elliptiques dégénérés

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A Widder's type theorem for the heat equation with nonlocal diffusion

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A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality

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Volume and distance comparison theorems for sub-Riemannian manifolds

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Perelman's entropy and doubling property on Riemannian manifolds

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A Note on the Boundedness of Riesz Transform for Some Subelliptic Operators

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Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries

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Asymptotic formulas for symmetric stable semigroups

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Nash type inequalities for fractional powers of non-negative self-adjoint operators

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Maximum principles, extension problem and inversion for nonlocal one-sided equations

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The nonlocal porous medium equation: Barenblatt profiles and other weak solutions

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Comparison results and steady states for the Fujita equation with fractional Laplacian.

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Some Theorems on Stable Processes

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Lectures on Fourier Integrals. (AM-42)

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Fourier Transforms. (AM-19)

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The boundary Harnack principle for the fractional Laplacian

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Representation of \(a\)-harmonic functions in Lipschitz domains

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Probabilistic proof of boundary Harnack principle for \(\alpha\)-harmonic functions

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Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains

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Heat kernel estimates for the fractional Laplacian with Dirichlet conditions

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Estimates of heat kernel of fractional Laplacian perturbed by gradient operators

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Gradient estimates for harmonic and \(q\)-harmonic functions of symmetric stable processes.

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Optimal existence and uniqueness theory for the fractional heat equation

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A concave—convex elliptic problem involving the fractional Laplacian

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Nonlocal heat equations: regularizing effect, decay estimates and Nash inequalities

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Higher Sobolev regularity for the fractional \(p\)-Laplace equation in the superquadratic case

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Higher Hölder regularity for the fractional \(p\)-Laplacian in the superquadratic case

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Some observations on the Green function for the ball in the fractional Laplace framework

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Nonlocal diffusion and applications

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Asymptotic mean value properties for fractional anisotropic operators

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Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions

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Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: a survey

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The influence of fractional diffusion in Fisher-KPP equations

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Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates

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Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions

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Regularity theory for parabolic nonlinear integral operators

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Obstacle-type problems for minimal surfaces

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Regularity of solutions to the parabolic fractional obstacle problem

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Nonlocal minimal surfaces

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Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

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Minimization of a fractional perimeter-Dirichlet integral functional

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An Extension Problem Related to the Fractional Laplacian

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Convergence of nonlocal threshold dynamics approximations to front propagation

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Fractional elliptic equations, Caccioppoli estimates and regularity

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Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation

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An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem

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Fractional Laplacian in conformal geometry

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Some Liouville theorems for the fractional Laplacian

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A direct method of moving planes for the fractional Laplacian

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Classification of solutions for an integral equation

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Existence results for the fractional Nirenberg problem

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Global heat kernel estimates for symmetric jump processes

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Nuovo tipo di condizione al contorno e nuovo metodo di trattazione per il problema generalizzato di dirichlet

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Weighted norm inequalities for maximal functions and singular integrals

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A pointwise estimate for fractionary derivatives with applications to partial differential equations

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A maximum principle applied to quasi-geostrophic equations

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A pointwise inequality for fractional Laplacians

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Best constants for Sobolev inequalities for higher order fractional derivatives

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Riesz transforms for $1\le p\le 2$

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Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes

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Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces

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Optimal Regularity and the Free Boundaryin the Parabolic Signorini Problem

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Obstacle Problems Involving the Fractional Laplacian

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Delaunay-type singular solutions for the fractional Yamabe problem

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A General Fractional Porous Medium Equation

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Boundary Harnack estimates in slit domains and applications to thin free boundary problems

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C^\infty regularity of certain thin free boundaries

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C1 + α local regularity of weak solutions of degenerate elliptic equations

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Nonlocal Harnack inequalities

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Local behavior of fractional \(p\)-minimizers

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Fractional Elliptic Problems with Critical Growth in the Whole of ℝn

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Qualitative properties of positive solutions to nonlocal critical problems involving the Hardy-Leray potential

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Graph properties for nonlocal minimal surfaces

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All functions are locally \(s\)-harmonic up to a small error

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Boundary behavior of nonlocal minimal surfaces

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Hitchhiker's guide to the fractional Sobolev spaces

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Global solution and smoothing effect for a non-local regularization of a hyperbolic equation.

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Fractional calculus for power functions and eigenvalues of the fractional Laplacian

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Eigenvalues of the fractional Laplace operator in the unit ball

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Regularity for the supercritical fractional Laplacian with drift

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The Wiener test for degenerate elliptic equations

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The local regularity of solutions of degenerate elliptic equations

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Entire $s$-harmonic functions are affine

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Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations

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Overdetermined problems with fractional laplacian

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Regularity and rigidity theorems for a class of anisotropic nonlocal operators

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A rigidity result for non-local semilinear equations

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Relativistic stability of matter. I

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Local Regularity for Parabolic Nonlocal Operators

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The Dirichlet problem for nonlocal operators

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Regularity theory for general stable operators: parabolic equations

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Harnack inequality for fractional sub-Laplacians in Carnot groups

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Radial fractional Laplace operators and Hessian inequalities

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On the measure and the structure of the free boundary of the lower dimensional obstacle problem

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Harmonic Analysis in Phase Space. (AM-122)

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An embedding theorem for sobolev spaces related to non-smooth vector fieldsand harnack inequality

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Une condition géométrique pour l'inégalité de Harnack. (A geometric condition for Harnack's inequality)

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An extension problem for the CR fractional Laplacian

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Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)

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Uniqueness of Radial Solutions for the Fractional Laplacian

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Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in \(n\) variabili

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Marcel Riesz in memoriam [November 16, 1886 Györ -- September 4, 1969 Lund]

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Second order parabolic equations in nonvariational form: Boundary Harnack principle and comparison theorems for nonnegative solutions

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Unique continuation for a class of elliptic operators which degenerate on a manifold of arbitrary codimension

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A Symmetry Result Related to Some Overdetermined Boundary Value Problems

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Unique continuation for elliptic operators: A geometric-variational approach

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Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem

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Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift

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An epiperimetric inequality approach to the regularity of the free boundary in the Signorini problem with variable coefficients

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Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian

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New monotonicity formulas and the optimal regularity in the Signorini problem with variable coefficients

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First Passage Times for Symmetric Stable Processes in Space

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Recent Progress on the Fractional Laplacian in Conformal Geometry

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Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties

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Table errata: Table of integrals, series, and products [corrected and enlarged edition, Academic Press, New York, 1980; MR 81g:33001] by I. S. Gradshteyn [I. S. Gradshteĭn] and I. M. Ryzhik

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Scattering matrix in conformal geometry

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Existence and convexity of solutions of the fractional heat equation

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Local and nonlocal boundary conditions for \(\mu\)-transmission and fractional elliptic pseudodifferential operators

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Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators

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Integration by parts and Pohozaev identities for space-dependent fractional-order operators

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Optimal regularity for the Signorini problem

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Extension à l'équation de la chaleur d'un théorème de A. Harnack

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Hypoelliptic second order differential equations

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Global Hölder regularity for the fractional \(p\)-Laplacian

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A class of integral equations and approximation of \(p\)-Laplace equations

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Starshapedness of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings

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Asymptotic symmetry for a class of nonlinear fractional reaction-diffusion equations

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The Dirichlet problem for the Kohn Laplacian on the Heisenberg group. I

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Boundary behavior of harmonic functions in non-tangentially accessible domains

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Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein)

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Higher regularity of the free boundary in the obstacle problem for the fractional Laplacian

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A priori estimates for integro-differential operators with measurable kernels

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A new formulation of Harnack's inequality for nonlocal operators

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Higher regularity of the free boundary in the elliptic Signorini problem

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The variable coefficient thin obstacle problem: Carleman inequalities

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The variable coefficient thin obstacle problem: optimal regularity and regularity of the regular free boundary

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An algebra of pseudo‐differential operators

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Non‐coercive boundary value problems

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Symmetric Stable Laws and Stable-Like Jump-Diffusions

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Traces of harmonic functions, capacities, and traces of symmetric Markov processes

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Uniform estimates for fundamental solutions associated with nonlocal Dirichlet forms

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Nonlocal equations with measure data

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Recent Developments in Nonlocal Theory

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Ten equivalent definitions of the fractional Laplace operator

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On the parabolic kernel of the Schrödinger operator

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Perron's method and Wiener's theorem for a nonlocal equation

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p-Harmonic Functions in the Plane

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Nonunique continuation for uniformly parabolic and elliptic equations in self-adjoint divergence form with Hölder continuous coefficients

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Variational Methods for Nonlocal Fractional Problems

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Classical Expansions and Their Relation to Conjugate Harmonic Functions

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Extension properties and boundary estimates for a fractional heat operator

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The fractional calculus. Theory and applications of differentiation and integration to arbitrary order

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Optimal regularity of solutions to the obstacle problem for the fractional Laplacian with drift

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On the generation of semigroups of linear operators

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Sulla soluzione generalizzata di Wiener per il primo problema di valori al contorno nel caso parabolico

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Qnique Continuation for

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Critical stationary Kirchhoff equations in \(\mathbb R^N\) involving nonlocal operators

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Mean Curvature, The Laplacian, and Soap Bubbles

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Darstellung der Eigenwerte von \(\Delta u+\lambda u=0\) durch ein Randintegral

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L'intégrale de Riemann-Liouville et le problème de Cauchy

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Nonlocal equations in bounded domains: a survey

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Obstacle problems for integro-differential operators: regularity of solutions and free boundaries

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Boundary Regularity, Pohozaev Identities and Nonexistence Results

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The Dirichlet problem for the fractional Laplacian: regularity up to the boundary

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The Pohozaev identity for the fractional Laplacian

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The development of fractional calculus 1695-1900

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Unique Continuation for Fractional Schrödinger Equations with Rough Potentials

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Density estimates for a variational model driven by the Gagliardo norm

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Ground state solutions for nonlinear fractional Schrödinger equations in $\mathbb {R}^N$RN

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A symmetry problem in potential theory

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The Brezis-Nirenberg result for the fractional Laplacian

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Regularity of the obstacle problem for a fractional power of the laplace operator

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Some Theorems Concerning 2-Dimensional Brownian Motion

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Problems in harmonic analysis related to curvature

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Extension Problem and Harnack's Inequality for Some Fractional Operators

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Regularity Theory and Extension Problem for Fractional Nonlocal Parabolic Equations and the Master Equation

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Analysis of the Laplacian on a complete Riemannian manifold

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The Brezis-Nirenberg type problem involving the square root of the Laplacian

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Partial differential equations. II: Qualitative studies of linear equations

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Regularity for a more general class of quasilinear equations

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The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion

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Asymptotic behaviour for the fractional heat equation in the Euclidean space

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Remark on the preceding paper of Serrin

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The method of orthogonal projection in potential theory

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Unique continuation for fractional orders of elliptic equations

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Identifiers

zbMATH Open document ID

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10.1090/conm/723/14569

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Mathematics Subject Classification ID

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zbMATH DE Number

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mardi Publication:5236846

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