{"title":"具有CDp⋅(m,K)曲率的加权图上p-拉普拉斯的Hamilton不等式","authors":"Yongtao Liu","doi":"10.1016/j.jmaa.2025.130036","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study Hamilton type gradient estimates for the <em>p</em>-Laplacian on weighted graphs. For <span><math><mi>p</mi><mo>></mo><mn>5</mn></math></span> and some additional assumptions, we derive a more general gradient estimate of Hamilton type for positive solutions to the <em>p</em>-Laplacian heat equation on finite graphs satisfying the <span><math><mi>C</mi><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow><mrow><msqrt><mrow><mo>⋅</mo></mrow></msqrt></mrow></msubsup><mo>(</mo><mi>m</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span> curvature. The analogous result is also proved for locally finite graphs with bounded weighted vertex degree. As an application of our main results, we show that the corresponding Harnack inequality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130036"},"PeriodicalIF":1.2000,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hamilton inequality for the p-Laplacian on weighted graphs with the CDp⋅(m,K) curvature\",\"authors\":\"Yongtao Liu\",\"doi\":\"10.1016/j.jmaa.2025.130036\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we study Hamilton type gradient estimates for the <em>p</em>-Laplacian on weighted graphs. For <span><math><mi>p</mi><mo>></mo><mn>5</mn></math></span> and some additional assumptions, we derive a more general gradient estimate of Hamilton type for positive solutions to the <em>p</em>-Laplacian heat equation on finite graphs satisfying the <span><math><mi>C</mi><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow><mrow><msqrt><mrow><mo>⋅</mo></mrow></msqrt></mrow></msubsup><mo>(</mo><mi>m</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span> curvature. The analogous result is also proved for locally finite graphs with bounded weighted vertex degree. As an application of our main results, we show that the corresponding Harnack inequality.</div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"555 1\",\"pages\":\"Article 130036\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X25008170\",\"RegionNum\":3,\"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":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25008170","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Hamilton inequality for the p-Laplacian on weighted graphs with the CDp⋅(m,K) curvature
In this paper, we study Hamilton type gradient estimates for the p-Laplacian on weighted graphs. For and some additional assumptions, we derive a more general gradient estimate of Hamilton type for positive solutions to the p-Laplacian heat equation on finite graphs satisfying the curvature. The analogous result is also proved for locally finite graphs with bounded weighted vertex degree. As an application of our main results, we show that the corresponding Harnack inequality.
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
• Probability
• Mathematical biology
• Combinatorics
• Mathematical physics.