Regularity estimates for elliptic nonlocal operators

Abstract

We study weak solutions to nonlocal equations governed by integrodifferential operators. Solutions are defined with the help of symmetric nonlocal bilinear forms. Throughout this work, our main emphasis is on operators with general, possibly singular, measurable kernels. We obtain regularity results which are robust with respect to the differentiability order of the equation. Furthermore, we provide a general tool for the derivation of Hölder a-priori estimates from the weak Harnack inequality. This tool is applicable for several local and nonlocal, linear and nonlinear problems on metric spaces. Another aim of this work is to provide comparability results for nonlocal quadratic forms.

43 pages, 1 figure

References in corpus (3)

• Nonlocal diffusion and applications
• Local behavior of fractional $p$-minimizers
• A T(1) theorem for fractional Sobolev spaces on domains

Cited by in corpus (18)

• Integro-Differential Elliptic Equations
• The Wiener criterion for nonlocal Dirichlet problems
• A general framework for nonlocal Neumann problems
• Global regularity results for non-homogeneous growth fractional problems
• Regularity estimates for fractional orthotropic $p$-Laplacians of mixed order
• Nonlocal operators related to nonsymmetric forms II: Harnack inequalities
• Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium
• On a Class of Nonlocal Obstacle Type Problems Related to the Distributional Riesz Fractional Derivative
• Local regularity for nonlocal equations with variable exponents
• Nonlocal complement value problem for a global in time parabolic equation
• Quadratic forms and Sobolev spaces of fractional order
• Elliptic Harnack inequalities for symmetric non-local Dirichlet forms
• Robust near-diagonal Green function estimates
• Homogenization of symmetric stable-like processes in stationary ergodic medium
• Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities
• On the strong maximum principle for nonlocal operators
• Nonlinear elliptic equations with integro-differential divergence form operators and measure data under sign condition on the nonlinearity
• Existence results for Cahn-Hilliard type systems driven by nonlocal integrodifferential operators with singular kernels