Regularity for parabolic integro-differential equations with very irregular kernels
Analysis of PDEs
2016-07-06 v1 Probability
Abstract
We prove H\"older regularity for a general class of parabolic integro-differential equations, which (strictly) includes many previous results. We present a proof which avoids the use of a convex envelop as well as give a new covering argument which is better suited to the fractional order setting. Our main result involves a class of kernels which may contain a singular measure, may vanish at some points, and are not required to be symmetric. This new generality of integro-differential operators opens the door to further applications of the theory, including some regularization estimates for the Boltzmann equation.
Cite
@article{arxiv.1412.3790,
title = {Regularity for parabolic integro-differential equations with very irregular kernels},
author = {Russell W. Schwab and Luis Silvestre},
journal= {arXiv preprint arXiv:1412.3790},
year = {2016}
}