English

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 pp-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 C1,1C^{1,1} domain. Furthermore we connect this dichotomy to the support of the boundary type Riesz measure related to the pp-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}
}