Regularity of the Free Boundary for a Bernoulli-Type Parabolic Problem with Variable Coefficients
Analysis of PDEs
2015-12-04 v1
Abstract
This paper studies the regularity of the free boundary for viscosity solutions to a parabolic Bernoulli-type free boundary problem with variable coefficients. The main result is that Lipschitz free boundaries are with a normal vector that varies with a H\"older modulus of continuity in both space and in time. As a consequence, the viscosity solution satisfies the free boundary problem in a classical sense.
Keywords
Cite
@article{arxiv.1512.00917,
title = {Regularity of the Free Boundary for a Bernoulli-Type Parabolic Problem with Variable Coefficients},
author = {Thomas Backing},
journal= {arXiv preprint arXiv:1512.00917},
year = {2015}
}