{"title":"Some rigidity results and asymptotic properties for solutions to semilinear elliptic P.D.E.","authors":"Matteo Rizzi , Panayotis Smyrnelis","doi":"10.1016/j.na.2024.113610","DOIUrl":null,"url":null,"abstract":"<div><p>We will present some rigidity results for solutions to semilinear elliptic equations of the form <span><math><mrow><mi>Δ</mi><mi>u</mi><mo>=</mo><msup><mrow><mi>W</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>W</mi></math></span> is a quite general potential with a local minimum and a local maximum. We are particularly interested in Liouville-type theorems and symmetry results, which generalise some known facts about the Cahn–Hilliard equation.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"247 ","pages":"Article 113610"},"PeriodicalIF":1.3000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24001299/pdfft?md5=a45788b8d984b525a97fb6104f87a266&pid=1-s2.0-S0362546X24001299-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24001299","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We will present some rigidity results for solutions to semilinear elliptic equations of the form , where is a quite general potential with a local minimum and a local maximum. We are particularly interested in Liouville-type theorems and symmetry results, which generalise some known facts about the Cahn–Hilliard equation.
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Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.
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