An epiperimetric inequality approach to the parabolic Signorini problem
Analysis of PDEs
2019-11-15 v3
Abstract
In this note, we use an epiperimetric inequality approach to study the regularity of the free boundary for the parabolic Signorini problem. We show that if the "vanishing order" of a solution at a free boundary point is close to or an even integer, then the solution is asymptotically homogeneous. Furthermore, one can derive a convergence rate estimate towards the asymptotic homogeneous solution. As a consequence, we obtain the regularity of the regular free boundary as well as the frequency gap.
Keywords
Cite
@article{arxiv.1810.11791,
title = {An epiperimetric inequality approach to the parabolic Signorini problem},
author = {Wenhui Shi},
journal= {arXiv preprint arXiv:1810.11791},
year = {2019}
}