{"title":"RCD(K,N)空间上 p-拉普拉斯的塔伦蒂型比较定理及其一些应用","authors":"Wenjing Wu","doi":"10.1016/j.na.2024.113631","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we prove a Talenti-type comparison theorem for the <span><math><mi>p</mi></math></span>-Laplacian with Dirichlet boundary conditions on open subsets of a normalized <span><math><mrow><mi>RCD</mi><mrow><mo>(</mo><mi>K</mi><mo>,</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> space with <span><math><mrow><mi>K</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>N</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span>. The obtained Talenti-type comparison theorem is sharp, rigid and stable with respect to measured Gromov–Hausdorff topology. As an application of such Talenti-type comparison, we establish a sharp and rigid reverse Hölder inequality for first eigenfunctions of the <span><math><mi>p</mi></math></span>-Laplacian and a related quantitative stability result.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"248 ","pages":"Article 113631"},"PeriodicalIF":1.3000,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Talenti-type comparison theorem for the p-Laplacian on RCD(K,N) spaces and some applications\",\"authors\":\"Wenjing Wu\",\"doi\":\"10.1016/j.na.2024.113631\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we prove a Talenti-type comparison theorem for the <span><math><mi>p</mi></math></span>-Laplacian with Dirichlet boundary conditions on open subsets of a normalized <span><math><mrow><mi>RCD</mi><mrow><mo>(</mo><mi>K</mi><mo>,</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> space with <span><math><mrow><mi>K</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>N</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span>. The obtained Talenti-type comparison theorem is sharp, rigid and stable with respect to measured Gromov–Hausdorff topology. As an application of such Talenti-type comparison, we establish a sharp and rigid reverse Hölder inequality for first eigenfunctions of the <span><math><mi>p</mi></math></span>-Laplacian and a related quantitative stability result.</p></div>\",\"PeriodicalId\":49749,\"journal\":{\"name\":\"Nonlinear Analysis-Theory Methods & Applications\",\"volume\":\"248 \",\"pages\":\"Article 113631\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-08-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Theory Methods & Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0362546X24001500\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24001500","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Talenti-type comparison theorem for the p-Laplacian on RCD(K,N) spaces and some applications
In this paper, we prove a Talenti-type comparison theorem for the -Laplacian with Dirichlet boundary conditions on open subsets of a normalized space with and . The obtained Talenti-type comparison theorem is sharp, rigid and stable with respect to measured Gromov–Hausdorff topology. As an application of such Talenti-type comparison, we establish a sharp and rigid reverse Hölder inequality for first eigenfunctions of the -Laplacian and a related quantitative stability result.
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