Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces

Abstract

We prove interior $H^{2s-\epsilon }$ regularity for weak solutions of linear elliptic integro-differential equations close to the fractional $s$-Laplacian. The result is obtained via intermediate estimates in Nikol'skii spaces, which are in turn carried out by means of an appropriate modification of the classical translation method by Nirenberg.

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• Weighted analytic regularity for the integral fractional Laplacian in polygons
• The Poisson equation from non-local to local
• Nonlocal complement value problem for a global in time parabolic equation
• Regularity of the solution to fractional diffusion, advection, reaction equations
• On the Calderon-Zygmund property of Riesz-transform type operators arising in nonlocal equations
• $H^{s,p}$ regularity theory for a class of nonlocal elliptic equations