Optimal Hölder regularity for solutions to Signorini-type obstacle problems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917903627976704 |
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| author | Lee, Ki-Ahm Lee, Se-Chan Schefer, Waldemar |
| author_facet | Lee, Ki-Ahm Lee, Se-Chan Schefer, Waldemar |
| contents | 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 Hölder 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Hölder regularity for solutions to Signorini-type obstacle problems Lee, Ki-Ahm Lee, Se-Chan Schefer, Waldemar Analysis of PDEs 35B65, 35J86, 35R35 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 Hölder 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. |
| title | Optimal Hölder regularity for solutions to Signorini-type obstacle problems |
| topic | Analysis of PDEs 35B65, 35J86, 35R35 |
| url | https://arxiv.org/abs/2501.16179 |