{"title":"Sharp sub-Gaussian upper bounds for subsolutions of Trudinger’s equation on Riemannian manifolds","authors":"Philipp Sürig","doi":"10.1016/j.na.2024.113641","DOIUrl":null,"url":null,"abstract":"<div><p>We consider on Riemannian manifolds the nonlinear evolution equation <span><span><span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>=</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>1</mn><mo>/</mo><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup><mo>)</mo></mrow><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>p</mi><mo>></mo><mn>1</mn></mrow></math></span>. This equation is also known as a doubly non-linear parabolic equation or Trudinger’s equation. We prove that weak subsolutions of this equation have a sub-Gaussian upper bound and prove that this upper bound is sharp for a specific class of manifolds including <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"249 ","pages":"Article 113641"},"PeriodicalIF":1.3000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24001603/pdfft?md5=d58d3972144f1e8175ec28d9bd63d444&pid=1-s2.0-S0362546X24001603-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/S0362546X24001603","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We consider on Riemannian manifolds the nonlinear evolution equation where . This equation is also known as a doubly non-linear parabolic equation or Trudinger’s equation. We prove that weak subsolutions of this equation have a sub-Gaussian upper bound and prove that this upper bound is sharp for a specific class of manifolds including .
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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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