Gevrey regularity for integro-differential operators

Abstract

We prove for some singular kernels $K(x,y)$ that viscosity solutions of the integro-differential equation ${\int }_{{\mathbb{R}}^n}\left[u(x+y)+u(x-y)-2u(x)\right]K(x,y)dy=f(x)$ locally belong to some Gevrey class if so does $f$. The fractional Laplacian equation is included in this framework as a special case.

15 pages

References in corpus (4)

• An extension problem related to the fractional Laplacian
• From the long jump random walk to the fractional Laplacian
• Some observations on the Green function for the ball in the fractional Laplace framework
• Convergence of nonlocal threshold dynamics approximations to front propagation

Cited by in corpus (5)

• Regularity theory and high order numerical methods for the (1d)-Fractional Laplacian
• Weighted analytic regularity for the integral fractional Laplacian in polygons
• Regularity of the solution to fractional diffusion, advection, reaction equations
• Analyticity for Solution of Integro-Differential Operators
• On the Analyticity of Critical Points of the Generalized Integral Menger Curvature in the Hilbert Case