Free boundary regularity for almost minimizers of the parabolic Signorini problem

Fuente: arXiv
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Autori principali: Jeon, Seongmin, Petrosyan, Arshak
Natura: Preprint
Pubblicazione: 2024
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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