{"title":"Existence of renormalized solutions for some degenerate and non-coercive elliptic equations","authors":"Y. Akdim, M. Belayachi, H. Hjiaj","doi":"10.21136/mb.2022.0061-21","DOIUrl":null,"url":null,"abstract":". This paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by where Ω is a bounded open set of R N ( N > 2) with 1 < p < N and f ∈ L 1 (Ω) , under some growth conditions on the function b ( · ) and d ( · ) , where c ( · ) is assumed to be in L N/ ( p − 1) (Ω) . We show the existence of renormalized solutions for this non-coercive elliptic equation, also, some regularity results will be concluded.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Bohemica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21136/mb.2022.0061-21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
. This paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by where Ω is a bounded open set of R N ( N > 2) with 1 < p < N and f ∈ L 1 (Ω) , under some growth conditions on the function b ( · ) and d ( · ) , where c ( · ) is assumed to be in L N/ ( p − 1) (Ω) . We show the existence of renormalized solutions for this non-coercive elliptic equation, also, some regularity results will be concluded.