The parabolic Harnack inequality for nonlocal equations
Analysis of PDEs
2024-01-26 v2 Probability
Abstract
We complete the local regularity program for weak solutions to linear parabolic nonlocal equations with bounded measurable coefficients. Within the variational framework we prove the parabolic Harnack inequality and H\"older regularity estimates. We discuss in detail the shortcomings of previous results in this direction. The key element of our approach is a fine study of the nonlocal tail term.
Cite
@article{arxiv.2303.05975,
title = {The parabolic Harnack inequality for nonlocal equations},
author = {Moritz Kassmann and Marvin Weidner},
journal= {arXiv preprint arXiv:2303.05975},
year = {2024}
}
Comments
to appear in Duke Mathematical Journal