{"title":"A strong maximum principle for mixed local and nonlocal p-Laplace equations","authors":"Bin Shang, Chao Zhang","doi":"10.3233/asy-221803","DOIUrl":null,"url":null,"abstract":"We establish a strong maximum principle for weak solutions of the mixed local and nonlocal p-Laplace equation − Δ p u + ( − Δ ) p s u = c ( x ) | u | p − 2 u in Ω , where Ω ⊂ R N is an open set, p ∈ ( 1 , ∞ ), s ∈ ( 0 , 1 ) and c ∈ C ( Ω ‾ ).","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asymptotic Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3233/asy-221803","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
We establish a strong maximum principle for weak solutions of the mixed local and nonlocal p-Laplace equation − Δ p u + ( − Δ ) p s u = c ( x ) | u | p − 2 u in Ω , where Ω ⊂ R N is an open set, p ∈ ( 1 , ∞ ), s ∈ ( 0 , 1 ) and c ∈ C ( Ω ‾ ).
期刊介绍：
The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
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