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arXiv · 2501.16179

Optimal H\"{o}lder regularity for solutions to Signorini-type obstacle problems

Ki-Ahm Lee·Se-Chan Lee·Waldemar Schefer
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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.

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Ki-Ahm Lee, Se-Chan Lee, Waldemar Schefer. 2025-01-27. Optimal H\"{o}lder regularity for solutions to Signorini-type obstacle problems. https://arxiv.org/abs/2501.16179

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