Free boundary regularity for almost minimizers of the parabolic Signorini problem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909382673956864 |
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| author | Jeon, Seongmin Petrosyan, Arshak |
| author_facet | Jeon, Seongmin Petrosyan, Arshak |
| contents | In this paper, we study the regularity of the "regular" part of the free boundary for almost minimizers in the parabolic Signorini problem with zero thin obstacle. This work is a continuation of our earlier research on the regularity of almost minimizers. We first establish the Weiss-type monotonicity formula by comparing almost minimizers with parabolically homogeneous replacements and utilizing conformal self-similar coordinates. Subsequently, by deriving the Almgren-type frequency formula and applying the epiperimetric inequality, we obtain the optimal growth near regular free boundary points and achieve the regularity of the regular set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06092 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free boundary regularity for almost minimizers of the parabolic Signorini problem Jeon, Seongmin Petrosyan, Arshak Analysis of PDEs 35R35 In this paper, we study the regularity of the "regular" part of the free boundary for almost minimizers in the parabolic Signorini problem with zero thin obstacle. This work is a continuation of our earlier research on the regularity of almost minimizers. We first establish the Weiss-type monotonicity formula by comparing almost minimizers with parabolically homogeneous replacements and utilizing conformal self-similar coordinates. Subsequently, by deriving the Almgren-type frequency formula and applying the epiperimetric inequality, we obtain the optimal growth near regular free boundary points and achieve the regularity of the regular set. |
| title | Free boundary regularity for almost minimizers of the parabolic Signorini problem |
| topic | Analysis of PDEs 35R35 |
| url | https://arxiv.org/abs/2411.06092 |