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

From MaRDI portal
Publication:2475979

DOI10.1007/s00222-007-0086-6zbMath1148.35097arXivmath/0702392OpenAlexW2168741104MaRDI QIDQ2475979

Luis A. Caffarelli, Sandro Salsa, Luis Silvestre

Publication date: 11 March 2008

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702392



Related Items

Local Lipschitz continuity of the inverse of the fractional \(p\)-Laplacian, Hölder type continuity and continuous dependence of solutions to associated parabolic equations on bounded domains, Boundary regularity for a degenerate elliptic equation with mixed boundary conditions, Singular perturbation problem in boundary/fractional combustion, Fractional elliptic equations, Caccioppoli estimates and regularity, Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian, Extension properties and boundary estimates for a fractional heat operator, Generic regularity of free boundaries for the obstacle problem, An epiperimetric inequality approach to the regularity of the free boundary in the Signorini problem with variable coefficients, Regularity of local minimizers of the interaction energy via obstacle problems, Existence of optimal solutions to Lagrange problems for ordinary control systems involving fractional Laplace operators, The structure of the singular set in the thin obstacle problem for degenerate parabolic equations, Optimal regularity for the Signorini problem and its free boundary, Optimal control of a nonlinear PDE governed by fractional Laplacian, Existence results for the fractional Nirenberg problem, Decay estimates for nonlocal problems via energy methods, The Dirichlet problem for the \(p\)-fractional Laplace equation, On the lack of controllability of fractional in time ODE and PDE, The variable coefficient thin obstacle problem: Carleman inequalities, Boundary regularity for fully nonlinear integro-differential equations, On the superlinear problems involving the fractional Laplacian, Classification of isolated singularities of positive solutions for Choquard equations, Analysis and approximation of a nonlocal obstacle problem, A regularity theory for intrinsic minimising fractional harmonic maps, Weyl and Marchaud derivatives: a forgotten history, Sign-changing solutions for non-local elliptic equations with asymptotically linear term, The obstacle problem for the fractional Laplacian with critical drift, Infinitely many solutions for non-local problems with broken symmetry, Extension problem and fractional operators: semigroups and wave equations, Regularity of solutions of the fractional porous medium flow, Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators, Optimal regularity for the thin obstacle problem with \(C^{0,\alpha }\) coefficients, Aperiodic fractional obstacle problems, On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent, (non)local and (non)linear free boundary problems, Infinitely many sign-changing solutions for the Brézis-Nirenberg problem involving the fractional Laplacian, Application of mountain pass theorem to superlinear equations with fractional Laplacian controlled by distributed parameters and boundary data, Value function regularity in option pricing problems under a pure jump model, A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian, Sharp Green function estimates for \(\Delta + \delta ^{\alpha /2}\) in \(C^{1,1}\) open sets and their applications, Comparison and sub-supersolution principles for the fractional \(p(x)\)-Laplacian, On the ground state solution for a critical fractional Laplacian equation, Solutions of fractional Laplacian equations and their Morse indices, Asymptotic behavior of stochastic fractional power dissipative equations on \(\mathbb{R}^n\), Ground state solutions of scalar field fractional Schrödinger equations, Fractional Laplacian in conformal geometry, Localization and vector spherical harmonics, Bahri invariants for fractional Nirenberg-type flows, Large deviation principle for empirical fields of log and Riesz gases, Equidistribution of jellium energy for Coulomb and Riesz interactions, Regularity in a one-phase free boundary problem for the fractional Laplacian, The Brezis-Nirenberg type problem involving the square root of the Laplacian, On a frequency function approach to the unique continuation principle, Hitchhiker's guide to the fractional Sobolev spaces, Left-inverses of fractional Laplacian and sparse stochastic processes, The multiplicity of nontrivial solutions for hemivariational inequalities involving nonlocal elliptic operators, Three weak solutions for nonlocal fractional Laplacian equations, Multiplicity of nontrivial solutions for a class of nonlocal elliptic operators systems of Kirchhoff type, Optimal regularity of solutions to the obstacle problem for the fractional Laplacian with drift, Thin obstacle problem: estimates of the distance to the exact solution, Existence of weak solutions for non-local fractional problems via Morse theory, \(L^q\)-extensions of \(L^p\)-spaces by fractional diffusion equations, Regularity theory for the fractional harmonic oscillator, Multiplicity of solutions for non-local elliptic equations driven by the fractional Laplacian, Obstacle problems and free boundaries: an overview, Dynamics of the 3-D fractional complex Ginzburg-Landau equation, Fractional semilinear Neumann problems arising from a fractional Keller-Segel model, Higher regularity of the free boundary in the elliptic Signorini problem, Uniform Hölder bounds for strongly competing systems involving the square root of the Laplacian, The obstacle problem for the infinity fractional Laplacian, Some notes on supersolutions of fractional \(p\)-Laplace equation, Fourier spectral approximations to the dynamics of 3D fractional complex Ginzburg-Landau equation, Periodic solutions for critical fractional problems, Ten equivalent definitions of the fractional Laplace operator, On the regularity of the non-dynamic parabolic fractional obstacle problem, Higher regularity of the free boundary in the parabolic Signorini problem, Weighted Poincaré inequality and heat kernel estimates for finite range jump processes, Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift, Least energy solutions for nonlinear Schrödinger equation involving the fractional Laplacian and critical growth, Variational inequalities for the fractional Laplacian, Morrey spaces in harmonic analysis, Nonexistence results for a class of fractional elliptic boundary value problems, Positive solutions of nonlinear problems involving the square root of the Laplacian, Comparison and regularity results for the fractional Laplacian via symmetrization methods, Nonlinear porous medium flow with fractional potential pressure, On the measure and the structure of the free boundary of the lower dimensional obstacle problem, Variational problems with free boundaries for the fractional Laplacian, Heat kernel estimates for the Dirichlet fractional Laplacian, A Liouville problem for the stationary fractional Navier-Stokes-Poisson system, The Navier-slip thin-film equation for 3D fluid films: existence and uniqueness, Trudinger-Moser type inequality and existence of solution for perturbed non-local elliptic operators with exponential nonlinearity, Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result, Properties of a frequency of Almgren type for harmonic functions in Carnot groups, Nodal sets of Steklov eigenfunctions, Nonlinear elliptic systems involving the fractional Laplacian in the unit ball and on a half space, On a nonlocal diffusion model with Neumann boundary conditions, Symmetric jump processes and their heat kernel estimates, A critical point theorem for perturbed functionals and low perturbations of differential and nonlocal systems, Almgren's frequency formula for an extension problem related to the anisotropic fractional Laplacian, Optimal regularity for the Signorini problem, Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions, VARIATIONAL ANALYSIS FOR FRACTIONAL EQUATIONS WITH VARIABLE EXPONENTS: EXISTENCE, MULTIPLICITY AND NONEXISTENCE RESULTS, Least-energy nodal solutions of nonlinear equations with fractional Orlicz–Sobolev spaces, The First Eigenvalue for Nonlocal Operators, On a Riemann–Liouville fractional analog of the Laplace operator with positive energy, The obstacle problem for nonlinear integro-differential operators, Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case, Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations, Sign-changing solutions for a class of zero mass nonlocal Schrödinger equations, The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation, Regularity for the fully nonlinear parabolic thin obstacle problem, Symmetry and monotonicity of positive solutions for a Choquard equation with the fractional Laplacian, Strong Competition versus Fractional Diffusion: The Case of Lotka-Volterra Interaction, Existence of solutions for nonlocal supercritical elliptic problems, Averaging principle for multiscale stochastic fractional Schrödinger-Korteweg-de Vries system, Fractional Orlicz-Sobolev embeddings, Free boundary regularity for almost every solution to the Signorini problem, Nonresonance and resonance problems for nonlocal elliptic equations with respect to the Fučik spectrum, An existence result for singular nonlocal fractional Kirchhoff–Schrödinger–Poisson system, Carleman estimates for Baouendi–Grushin operators with applications to quantitative uniqueness and strong unique continuation, Infinitely many solutions for a class of fractional Robin problems with variable exponents, Multiple periodic solutions of a class of fractional Laplacian equations, On a class of nonlocal obstacle type problems related to the distributional Riesz fractional derivative, Nonlocal Tug-of-War and the Infinity Fractional Laplacian, Improved regularity of second derivatives for subharmonic functions, A note on monotonicity and Bochner formulas in Carnot groups, Dual characterization of fractional capacity via solution of fractional p‐Laplace equation, Application of capacities to space–time fractional dissipative equations I: regularity and the blow-up set, On a weak maximum principle for a class of fractional diffusive equations, Unnamed Item, On a weighted two-phase boundary obstacle problem, Stochastic 3D Leray-\(\alpha\) model with fractional dissipation, On fractional Orlicz‑Sobolev spaces, \(C^{2, \alpha}\) regularity of free boundaries in parabolic non-local obstacle problems, Some free boundary problems involving non-local diffusion and aggregation, Convergence rates for the classical, thin and fractional elliptic obstacle problems, Global existence and convergence results for a class of nonlinear time fractional diffusion equation, On a class of non-local elliptic equations with asymptotically linear term, Numerical methods for fractional diffusion, An epiperimetric inequality for the lower dimensional obstacle problem, Homogenization of non-local nonlinear p-Laplacian equation with variable index and periodic structure, Fast operator splitting methods for obstacle problems, External optimal control of fractional parabolic PDEs, Regularity of the minimiser of one-dimensional interaction energies, Commutators with fractional differentiation for second-order elliptic operators on ℝn, The obstacle problem for a higher order fractional Laplacian, Optimal regularity for supercritical parabolic obstacle problems, The forbidden region for random zeros: Appearance of quadrature domains, An obstacle problem arising from American options pricing: regularity of solutions, Fractional double phase Robin problem involving variable‐order exponents and logarithm‐type nonlinearity, Boundary estimates and a Wiener criterion for the fractional Laplacian, Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian, Hopf type lemmas for subsolutions of integro-differential equations, Regularity of the singular set in the fully nonlinear obstacle problem, Optimal Regularity and the Free Boundaryin the Parabolic Signorini Problem, Necessary optimality conditions for Lagrange problems involving ordinary control systems described by fractional Laplace operators, Unnamed Item, Decay estimates of nonlocal diffusion equations in some particle systems, Infinitely many solutions for fractional Kirchhoff-Schrödinger-Poisson systems, Properties of the linear non-local Stokes operator and its application, Robin fractional problems with symmetric variable growth, Space like strong unique continuation for sublinear parabolic equations, Unnamed Item, Unnamed Item, The obstacle problem for a fractional Monge–Ampère equation, Quantitative Estimate of the Continuum Approximations of Interacting Particle Systems in One Dimension, Optimal control of systems governed by fractional Laplacian in the minimax framework, NEXT ORDER ASYMPTOTICS AND RENORMALIZED ENERGY FOR RIESZ INTERACTIONS, Ground states for superlinear fractional Schrödinger equations in R^N, Some integrability estimates for solutions of the fractional p-Laplace equation, Optimal Regularity in Rooftop-Like Obstacle Problem, Contact of a thin free boundary with a fixed one in the Signorini problem, Extension Problem and Harnack's Inequality for Some Fractional Operators, Unnamed Item, Fractional Gaussian fields: a survey, Regularity for obstacle problems in infinite dimensional Hilbert spaces, Infinitely many solutions for non-local elliptic non-degeneratep-Kirchhoff equations with critical exponent, Existence, non-existence and blow-up behaviour of minimizers for the mass-critical fractional non-linear Schrödinger equations with periodic potentials, Ground states solutions for a non-linear equation involving a pseudo-relativistic Schrödinger operator, Symmetry of positive solutions for equations involving higher order fractional Laplacian, Nodal solutions for the fractional Yamabe problem on Heisenberg groups, Global heat kernel estimates for symmetric jump processes, Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations, External optimal control of nonlocal PDEs, A uniqueness principle for up ≤ (−Δ)α 2u in the Euclidean space, Unnamed Item, The Dirichlet problem for the logarithmic Laplacian, Fractional thoughts, Boundary regularity for the free boundary in the one-phase problem, The regular free boundary in the thin obstacle problem for degenerate parabolic equations, Homogenization of Random Fractional Obstacle Problems via Γ-Convergence, Boundary Harnack principle for $Δ+ Δ^{𝛼/2}$, Linear and nonlinear fractional elliptic problems, The Harnack inequality for a class of nonlocal parabolic equations, Laguerre operator and its associated weighted Besov and Triebel-Lizorkin spaces, Ground States of some Fractional Schrödinger Equations on ℝN, Almost minimizers for certain fractional variational problems, The Two-Phase Fractional Obstacle Problem, Dirichlet heat kernel estimates for rotationally symmetric Lévy processes, Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations, Inverse problem for a nonlocal diffuse optical tomography equation, Nonlocal equations with gradient constraints, Higher regularity of the free boundary in the obstacle problem for the fractional heat operator, The sparse representation related with fractional heat equations, Molecular decompositions of homogeneous Besov type spaces for Laguerre function expansions and applications, Obstacle problems for integro-differential operators with partially vanishing kernels, Unnamed Item, Gamma-convergence of generalized gradient flows with conjugate type, \(H^{1+ \alpha}\) estimates for the fully nonlinear parabolic thin obstacle problem, The variable coefficient thin obstacle problem: optimal regularity and regularity of the regular free boundary, The two membranes problem for different operators, Variational inequalities for the spectral fractional Laplacian, Least energy solutions of nonlinear Schrödinger equations involving the fractional Laplacian and potential wells, Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations, Solutions for the problems involving fractional Laplacian and indefinite potentials, Infinitely many positive solutions for a nonlocal problem with competing potentials, Concentrated solutions for a critical nonlocal problem, A class of time-fractional Dirac type operators, Normalized solutions to a kind of fractional Schrödinger equation with a critical nonlinearity, The local structure of the free boundary in the fractional obstacle problem, Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem, The thin obstacle problem for some variable coefficient degenerate elliptic operators, Foreword to the special issue ``Contemporary PDEs between theory and modeling, Regularity results for a penalized boundary obstacle problem, Higher regularity of the free boundary in the obstacle problem for the fractional Laplacian, Mountain pass and linking type sign-changing solutions for nonlinear problems involving the fractional Laplacian, Heat kernels for non-symmetric diffusion operators with jumps, Local uniqueness and periodicity for the prescribed scalar curvature problem of fractional operator in \({\mathbb {R}}^{N}\), Estimates of damped fractional wave equations, Multiplicity results for fractional systems crossing high eigenvalues, Optimal regularity and structure of the free boundary for minimizers in cohesive zone models, Boundary singularity of Choquard equation in the half space, How a minimal surface leaves a thin obstacle, Existence and multiplicity of weak positive solutions to a class of fractional Laplacian with a singular nonlinearity, Solutions for conformally invariant fractional Laplacian equations with multi-bumps centered in lattices, Basic results of fractional Orlicz-Sobolev space and applications to non-local problems, On a fractional Schrödinger equation with periodic potential, Optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian, On the nodal set of solutions to degenerate or singular elliptic equations with an application to \(s\)-harmonic functions, Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators, Rigidity results for nonlocal phase transitions in the Heisenberg group \(\mathbb{H}\), Uniform Hölder regularity with small exponent in competition-fractional diffusion systems, A perturbation result for the \(Q_{\gamma}\) curvature problem on \(\mathbb S^n\), On a differential inclusion involving Dirichlet-Laplace operators of fractional orders, Nodal and multiple solutions of nonlinear problems involving the fractional Laplacian, Optimal configuration and symmetry breaking phenomena in the composite membrane problem with fractional Laplacian, Maximum principle for the space-time fractional conformable differential system involving the fractional Laplace operator, On solvability of integro-differential equations, Ground state solutions for nonlinear fractional Kirchhoff-Schrödinger-Poisson systems, Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation, A two phase boundary obstacle-type problem for the bi-Laplacian, Semilinear elliptic equations for the fractional Laplacian with Hardy potential, Liouville theorems for fractional parabolic equations, On a fractional thin film equation, Regularity for the nonlinear Signorini problem, The sliding method for the nonlocal Monge-Ampère operator, The spectral method for long-time behavior of a fractional power dissipative system, New monotonicity formulas and the optimal regularity in the Signorini problem with variable coefficients, The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets, Existence and multiplicity of solutions for nonlinear elliptic problems with the fractional Laplacian, The structure of the free boundary in the fully nonlinear thin obstacle problem, Existence and uniqueness of positive solution for a fractional Dirichlet problem with combined nonlinear effects in bounded domains, On nodal solutions of the fractional Choquard equation, Realization of the fractional Laplacian with nonlocal exterior conditions via forms method, Stabilization of fractional evolution systems with memory, On the Hölder regularity for solutions of integro-differential equations like the anisotropic fractional Laplacian, Qualitative analysis of solutions of obstacle elliptic inclusion problem with fractional Laplacian, Some existence results for variational inequalities with nonlocal fractional operators, On a class of nonvariational problems in fractional Orlicz-Sobolev spaces, Identifying an unknown source term in a time-space fractional parabolic equation, Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian, Obstacle problems for integro-differential operators: higher regularity of free boundaries, On fractional Orlicz-Sobolev spaces, Dynamics of non-autonomous fractional reaction-diffusion equations on \(\mathbb{R}^N\) driven by multiplicative noise, The concentration-compactness principles for \(W^{s,p(\cdot,\cdot)}(\mathbb{R}^N)\) and application, Harnack inequality for fractional sub-Laplacians in Carnot groups, Almost minimizers for the thin obstacle problem, The fractional obstacle problem with drift: higher regularity of free boundaries, Extension technique for functions of diffusion operators: a stochastic approach, On the strong unique continuation property of a degenerate elliptic operator with Hardy-type potential, Characterizing compact coincidence sets in the thin obstacle problem and the obstacle problem for the fractional Laplacian, Regularity of free boundaries in obstacle problems for integro-differential operators, Interior regularity estimates for a degenerate elliptic equation with mixed boundary conditions, Nonexistence of positive solutions for an indefinite fractional \(p\)-Laplacian equation, Existence of a solution to a nonlocal Schrödinger system problem in fractional modular spaces, A limiting obstacle type problem for the inhomogeneous \(p\)-fractional Laplacian, Symmetry of positive solutions for systems of fractional Hartree equations, Speed-up of reaction-diffusion fronts by a line of fast diffusion, Multiple of solutions for nonlocal elliptic equations with critical exponent driven by the Fractional \(p\)-Laplacian of order \(s\), Higher regularity for the Signorini problem for the homogeneous, isotropic Lamé system, The thin obstacle problem: a survey, Necessary and sufficient conditions for the bounds of the commutators with fractional differentiations and BMO-Sobolev spaces on weighted Lebesgue space, Nonlocal Harnack inequalities for nonlocal heat equations, On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians, Optimal control of the coefficient for the regional fractional \(p\)-Laplace equation: approximation and convergence, The Boundary Harnack principle for nonlocal elliptic operators in non-divergence form, Extension of \(Q\) type spaces related with weights via \(s\)-harmonic equations and applications, Existence of multiple non-trivial solutions for a nonlocal problem, Radial symmetry for weak positive solutions of fractional Laplacian with a singular nonlinearity, Blow-up solutions to the Cauchy problem of a fractional reaction-diffusion system, Equations involving fractional Laplacian operator: compactness and application, Periodic solutions for a pseudo-relativistic Schrödinger equation, The obstacle problem at zero for the fractional \(p\)-Laplacian, Saddle solutions for the fractional Choquard equation, Boundary estimates for solutions to linear degenerate parabolic equations, Obstacle problems for integro-differential operators: regularity of solutions and free boundaries, Regional fractional Laplacians: boundary regularity



Cites Work