English

Analyticity for Solution of Integro-Differential Operators

Analysis of PDEs 2020-09-17 v1

Abstract

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

Cite

@article{arxiv.2009.07673,
  title  = {Analyticity for Solution of Integro-Differential Operators},
  author = {Simon Blatt},
  journal= {arXiv preprint arXiv:2009.07673},
  year   = {2020}
}
R2 v1 2026-06-23T18:35:07.336Z