Gradient estimates for a class of anisotropic nonlocal operators
Analysis of PDEs
2018-09-28 v2
Abstract
Using a classical technique introduced by Achi E. Brandt for elliptic equations, we study a general class of nonlocal equations obtained as a superposition of classical and fractional operators in different variables. We obtain that the increments of the derivative of the solution in the direction of a variable experiencing classical diffusion are controlled linearly, with a logarithmic correction. From this, we obtain H\"older estimates for the solution.
Cite
@article{arxiv.1809.08674,
title = {Gradient estimates for a class of anisotropic nonlocal operators},
author = {Alberto Farina and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1809.08674},
year = {2018}
}