Regularity of the free boundary for a parabolic cooperative system
Analysis of PDEs
2021-06-09 v1
Abstract
In this paper we study the following parabolic system \begin{equation*} \Delta \u -\partial_t \u =|\u|^{q-1}\u\,\chi_{\{ |\u|>0 \}}, \qquad \u = (u^1, \cdots , u^m) \ , \end{equation*} with free boundary . For , we prove optimal growth rate for solutions \u to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is in space directions and half-Lipschitz in the time direction.
Keywords
Cite
@article{arxiv.2106.04135,
title = {Regularity of the free boundary for a parabolic cooperative system},
author = {Gohar Aleksanyan and Morteza Fotouhi and Henrik Shahgholian and Georg S. Weiss},
journal= {arXiv preprint arXiv:2106.04135},
year = {2021}
}