{"title":"Weighted Sobolev Type Inequalities in a Smooth Metric Measure Space","authors":"Pengyan Wang, Huiting Chang","doi":"10.1007/s44198-024-00168-2","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we obtain weighted Sobolev type inequalities with explicit constants that extend the inequalities obtained by Guo et al. (Math Res Lett 28(5):1419–1439, 2021) in the Riemannian setting. As an application, we prove some new logarithmic Sobolev type inequalities in some smooth metric measure spaces.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"175 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s44198-024-00168-2","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we obtain weighted Sobolev type inequalities with explicit constants that extend the inequalities obtained by Guo et al. (Math Res Lett 28(5):1419–1439, 2021) in the Riemannian setting. As an application, we prove some new logarithmic Sobolev type inequalities in some smooth metric measure spaces.
期刊介绍：
Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles.
Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics.
The main subjects are:
-Nonlinear Equations of Mathematical Physics-
Quantum Algebras and Integrability-
Discrete Integrable Systems and Discrete Geometry-
Applications of Lie Group Theory and Lie Algebras-
Non-Commutative Geometry-
Super Geometry and Super Integrable System-
Integrability and Nonintegrability, Painleve Analysis-
Inverse Scattering Method-
Geometry of Soliton Equations and Applications of Twistor Theory-
Classical and Quantum Many Body Problems-
Deformation and Geometric Quantization-
Instanton, Monopoles and Gauge Theory-
Differential Geometry and Mathematical Physics
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