Fractional thoughts

DOI10.1090/conm/723/14569zbMath1423.35397arXiv1712.03347OpenAlexW2796280365MaRDI QIDQ5236846

Nicola Garofalo

Publication date: 16 October 2019

Published in: New Developments in the Analysis of Nonlocal Operators (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.03347

Mathematics Subject Classification ID

Fractional partial differential equations (35R11)

Related Items (55)

Quantitative normal approximations for the stochastic fractional heat equation ⋮ Nonradiality of second eigenfunctions of the fractional Laplacian in a ball ⋮ The structure of the singular set in the thin obstacle problem for degenerate parabolic equations ⋮ Fractional eigenvalues in Orlicz spaces with no \(\Delta_2\) condition ⋮ The thin obstacle problem for some variable coefficient degenerate elliptic operators ⋮ Fractional convexity ⋮ Regularity for parabolic systems with critical growth in the gradient and applications ⋮ Feeling the heat in a group of Heisenberg type ⋮ Fractional Laplacians on ellipsoids ⋮ Symmetrization for fractional elliptic problems: a direct approach ⋮ Lifshitz tails for the fractional Anderson model ⋮ \(L^p\) estimates for the Caffarelli-Silvestre extension operators ⋮ Nonlocal isoperimetric inequalities for Kolmogorov-Fokker-Planck operators ⋮ Harmonic extension technique for non-symmetric operators with completely monotone kernels ⋮ Nonlinear nonlocal Douglas identity ⋮ Stein-Weiss-Adams inequality on Morrey spaces ⋮ Pohozaev-type identities for a pseudo-relativistic Schrödinger operator and applications ⋮ On BMO and Hardy regularity estimates for a class of non-local elliptic equations ⋮ Segal–Bargmann transforms and holomorphic Sobolev spaces of fractional order ⋮ Computation of power law equilibrium measures on balls of arbitrary dimension ⋮ Semilinear nonlocal elliptic equations with source term and measure data ⋮ Blowing-up solutions of differential equations with shifts: a survey ⋮ Minimal Ws,ns$W^{s,\frac{n}{s}}$‐harmonic maps in homotopy classes ⋮ Asymptotic decay of solutions for sublinear fractional Choquard equations ⋮ A heat equation approach to intertwining ⋮ Oscillatory phenomena for higher-order fractional Laplacians ⋮ Some inequalities for the Fourier transform and their limiting behaviour ⋮ Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds ⋮ Sharp Li-Yau inequalities for Dunkl harmonic oscillators ⋮ Global endpoint regularity estimates for the fractional Dirichlet problem ⋮ The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour ⋮ Critical functions and blow-up asymptotics for the fractional Brezis-Nirenberg problem in low dimension ⋮ Li-Yau inequalities for general non-local diffusion equations via reduction to the heat kernel ⋮ On the Harnack inequality for antisymmetric \(s\)-harmonic functions ⋮ Long-range Phase Coexistence Models: Recent Progress on the Fractional Allen-Cahn Equation ⋮ Two classical properties of the Bessel quotient 𝐼_{𝜈+1}/𝐼_{𝜈} and their implications in pde’s ⋮ Higher-order fractional Laplacians: An overview ⋮ Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness ⋮ Growing solutions of the fractional \(p\)-Laplacian equation in the fast diffusion range ⋮ Symmetry and monotonicity of a nonlinear Schrödinger equation involving the fractional Laplacian ⋮ Functional inequalities for a class of nonlocal hypoelliptic equations of Hörmander type ⋮ Calderon-Zygmund type estimates for nonlocal PDE with Hölder continuous kernel ⋮ Liouville theorem involving the uniformly nonlocal operator ⋮ Some extension results for nonlocal operators and applications ⋮ On the fractional Landis conjecture ⋮ Lifshitz tails for random diagonal perturbations of Laurent matrices ⋮ The Harnack inequality for a class of nonlocal parabolic equations ⋮ Nonlocal complement value problem for a global in time parabolic equation ⋮ Asymptotic mean value formulas, nonlocal space-time parabolic operators and anomalous tug-of-war games ⋮ Space-like strong unique continuation for some fractional parabolic equations ⋮ A class of nonlocal hypoelliptic operators and their extensions ⋮ Cauchy problem for a fractional anisotropic parabolic equation in anisotropic Hölder spaces ⋮ On local regularity estimates for fractional powers of parabolic operators with time-dependent measurable coefficients ⋮ Integral operators defined ``up to a polynomial ⋮ Global existence and decay estimates for the classical solution of fractional attraction-repulsion chemotaxis system

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