Existence and regularity results for the penalized thin obstacle problem with variable coefficients
Analysis of PDEs
2020-05-13 v1
Abstract
In this paper we give a comprehensive treatment of a two-penalty boundary obstacle problem for a divergence form elliptic operator, motivated by applications to fluid dynamics and thermics. Specifically, we prove existence, uniqueness and optimal regularity of solutions, and establish structural properties of the free boundary. The proofs are based on tailor-made monotonicity formulas of Almgren, Weiss, and Monneau-type, combined with the classical theory of oblique derivative problems.
Cite
@article{arxiv.2005.05524,
title = {Existence and regularity results for the penalized thin obstacle problem with variable coefficients},
author = {Donatella Danielli and Brian Krummel},
journal= {arXiv preprint arXiv:2005.05524},
year = {2020}
}