{"title":"An epiperimetric inequality for odd frequencies in the thin obstacle problem","authors":"Matteo Carducci, Bozhidar Velichkov","doi":"arxiv-2409.12110","DOIUrl":null,"url":null,"abstract":"We prove an epiperimetric inequality for the thin obstacle Weiss' energy with\nodd frequencies and we apply it to solutions to the thin obstacle problem with\ngeneral $C^{k,\\gamma}$ obstacle. In particular, we obtain the rate of\nconvergence of the blow-up sequences at points of odd frequencies and the\nregularity of the strata of the corresponding contact set. We also recover the\nfrequency gap for odd frequencies obtained by Savin and Yu.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"43 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.12110","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We prove an epiperimetric inequality for the thin obstacle Weiss' energy with
odd frequencies and we apply it to solutions to the thin obstacle problem with
general $C^{k,\gamma}$ obstacle. In particular, we obtain the rate of
convergence of the blow-up sequences at points of odd frequencies and the
regularity of the strata of the corresponding contact set. We also recover the
frequency gap for odd frequencies obtained by Savin and Yu.