Analyticity for Solution of Integro-Differential Operators

Abstract

We prove that for a certain class of kernels $K(y)$ that viscosity solutions of the integro-differential equation $${\int }_{{\mathbb{R}}^n}(u(x+y)-2u(x)+u(x-y))K(y)dy=f(x,u(x))$$ are locally analytic if $f$ is an analytic function. This extends the result of Albanese, Fiscella, Valdinoci that such solutions belong to certain Gevrey classes.

References in corpus (1)

• Gevrey regularity for integro-differential operators