Boundary behavior of solutions to the parabolic p-Laplace equation II
Analysis of PDEs
2020-01-22 v2
Abstract
This paper is the second installment in a series of papers concerning the boundary behavior of solutions to the -parabolic equations. In this paper we are interested in the short time behavior of the solutions, which is in contrast with much of the literature, where all results require a waiting time. We prove a dichotomy about the decay-rate of non-negative solutions vanishing on the lateral boundary in a cylindrical domain. Furthermore we connect this dichotomy to the support of the boundary type Riesz measure related to the -parabolic equation in NTA-domains, which has consequences for the continuation of solutions.
Keywords
Cite
@article{arxiv.1710.06616,
title = {Boundary behavior of solutions to the parabolic p-Laplace equation II},
author = {Benny Avelin},
journal= {arXiv preprint arXiv:1710.06616},
year = {2020}
}