Optimal boundary regularity for fast diffusion equations in bounded domains
Analysis of PDEs
2021-07-06 v3
Abstract
We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains. This solves a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical regimes. Our proof of the a priori estimates uses a geometric type structure of the fast diffusion equations, where an important ingredient is an evolution equation for a curvature-like quantity.
Cite
@article{arxiv.1910.05160,
title = {Optimal boundary regularity for fast diffusion equations in bounded domains},
author = {Tianling Jin and Jingang Xiong},
journal= {arXiv preprint arXiv:1910.05160},
year = {2021}
}
Comments
This is a much improved version of the older manuscript, thanks to the suggestions of the anonymous referee. The main revision is that we added three appendices to provide supplementary materials for the linear equation part. Also, Corollary 1.4 is improved from the suggestions of the anonymous referee