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 (2)

• From the long jump random walk to the fractional Laplacian
• Convergence of nonlocal threshold dynamics approximations to front propagation