H\"older estimates for parabolic operators on domains with rough boundary
Analysis of PDEs
2015-03-25 v1
Abstract
We investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness and ellipticity on the coefficient function and very mild conditions on the geometry of the domain, including a very weak compatibility condition between the Dirichlet boundary part and its complement, we prove H\"older continuity of the solution in space and time.
Keywords
Cite
@article{arxiv.1503.07035,
title = {H\"older estimates for parabolic operators on domains with rough boundary},
author = {K. Disser and A. F. M. ter Elst and J. Rehberg},
journal= {arXiv preprint arXiv:1503.07035},
year = {2015}
}
Comments
1 figure