{"title":"Lipschitz continuity results for a class of obstacle problems","authors":"Carlo Benassi, Michele Caselli","doi":"10.4171/rlm/885","DOIUrl":null,"url":null,"abstract":". We prove Lipschitz continuity results for solutions to a class of obstacle problems under standard growth conditions of p − type, p ≥ 2. The main novelty is the use of a linearization technique going back to [28] in order to interpret our constrained minimizer as a solution to a nonlinear elliptic equation, with a bounded right hand side. This lead us to start a Moser iteration scheme which provides the L ∞ bound for the gradient. The application of a recent higher differentiability result [24] allows us to simplify the procedure of the identification of the Radon measure in the linearization technique employed in [32]. To our knowdledge, this is the first result for non-automonous functionals with standard growth conditions in the direction of the Lipschitz regularity.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2020-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/rlm/885","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti Lincei-Matematica e Applicazioni","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/rlm/885","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 6
Abstract
. We prove Lipschitz continuity results for solutions to a class of obstacle problems under standard growth conditions of p − type, p ≥ 2. The main novelty is the use of a linearization technique going back to [28] in order to interpret our constrained minimizer as a solution to a nonlinear elliptic equation, with a bounded right hand side. This lead us to start a Moser iteration scheme which provides the L ∞ bound for the gradient. The application of a recent higher differentiability result [24] allows us to simplify the procedure of the identification of the Radon measure in the linearization technique employed in [32]. To our knowdledge, this is the first result for non-automonous functionals with standard growth conditions in the direction of the Lipschitz regularity.
期刊介绍:
The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.