非局部对抛物方程解的荷尔德连续性的微扰方法

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-03-15 DOI:10.1007/s00028-024-00949-8

Alireza Tavakoli

{"title":"非局部对抛物方程解的荷尔德连续性的微扰方法","authors":"Alireza Tavakoli","doi":"10.1007/s00028-024-00949-8","DOIUrl":null,"url":null,"abstract":"We study local boundedness and Hölder continuity of a parabolic equation involving the fractional p-Laplacian of order s, with \\(0<s<1\\), \\(2\\le p < \\infty \\), with a general right-hand side. We focus on obtaining precise Hölder continuity estimates. The proof is based on a perturbative argument using the already known Hölder continuity estimate for solutions to the equation with zero right-hand side.","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A perturbative approach to Hölder continuity of solutions to a nonlocal p-parabolic equation\",\"authors\":\"Alireza Tavakoli\",\"doi\":\"10.1007/s00028-024-00949-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study local boundedness and Hölder continuity of a parabolic equation involving the fractional p-Laplacian of order s, with \\\\(0<s<1\\\\), \\\\(2\\\\le p < \\\\infty \\\\), with a general right-hand side. We focus on obtaining precise Hölder continuity estimates. The proof is based on a perturbative argument using the already known Hölder continuity estimate for solutions to the equation with zero right-hand side.\",\"PeriodicalId\":51083,\"journal\":{\"name\":\"Journal of Evolution Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Evolution Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00028-024-00949-8\",\"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 Evolution Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00028-024-00949-8","RegionNum":3,"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

摘要

我们研究了一个涉及阶数为 s 的分数 p-Laplacian 的抛物方程的局部有界性和霍尔德连续性，该方程有一个一般的右边：\(0<s<1\), \(2\le p < \infty \)。我们的重点是获得精确的霍尔德连续性估计。证明是基于一个扰动论证，使用已经知道的对方程右边为零的解的霍尔德连续性估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A perturbative approach to Hölder continuity of solutions to a nonlocal p-parabolic equation

We study local boundedness and Hölder continuity of a parabolic equation involving the fractional p-Laplacian of order s, with \(0<s<1\), \(2\le p < \infty \), with a general right-hand side. We focus on obtaining precise Hölder continuity estimates. The proof is based on a perturbative argument using the already known Hölder continuity estimate for solutions to the equation with zero right-hand side.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators