Regularity theory for singular nonlocal diffusion equations
Analysis of PDEs
2017-10-09 v1
Abstract
We prove continuity for bounded weak solutions of a nonlinear nonlocal parabolic type equation associated to a Dirichlet form with a rough kernel. The equation is allowed to be singular at the level zero, and solutions may change sign. If the nonlinearity in the equation does not oscillate too much at the origin, the solution is proved to be moreover H\"older continuous. The results are new even when the Dirichlet form is the one corresponding to the fractional Laplacian.
Keywords
Cite
@article{arxiv.1710.02303,
title = {Regularity theory for singular nonlocal diffusion equations},
author = {Arturo de Pablo and Fernando Quirós and Ana Rodríguez},
journal= {arXiv preprint arXiv:1710.02303},
year = {2017}
}