Optimal H\"{o}lder regularity for solutions to Signorini-type obstacle problems
Analysis of PDEs
2025-01-28 v1
Abstract
We study the existence, uniqueness, and regularity of weak solutions to a class of obstacle problems, where the obstacle condition can be imposed on a subset of the domain. In particular, we establish the optimal H\"older regularity for Signorini-type problems, that is, the obstacle condition is imposed only on a subset of codimension one. For this purpose, we employ capacities, Alt--Caffarelli--Friedman-type and Almgren-type monotonicity formulae, and investigate an associated mixed boundary value problem. Further, we apply this problem to study classical obstacle problems for irregular obstacles.
Cite
@article{arxiv.2501.16179,
title = {Optimal H\"{o}lder regularity for solutions to Signorini-type obstacle problems},
author = {Ki-Ahm Lee and Se-Chan Lee and Waldemar Schefer},
journal= {arXiv preprint arXiv:2501.16179},
year = {2025}
}
Comments
35 pages, 1 figure