{"title":"Hölder p(x)-拉普拉斯方程解的连续性","authors":"A. Lyaghfouri","doi":"10.3336/gm.57.1.03","DOIUrl":null,"url":null,"abstract":"We show that bounded solutions of the quasilinear elliptic equation\n\\(\\Delta_{p(x)} u=g+div(\\textbf{F})\\) are locally Hölder continuous\nprovided that the functions \\(g\\) and \\(\\textbf{F}\\) are in suitable\nLebesgue spaces.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hölder continuity for the solutions of the p(x)-Laplace equation\\nwith general right-hand side\",\"authors\":\"A. Lyaghfouri\",\"doi\":\"10.3336/gm.57.1.03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that bounded solutions of the quasilinear elliptic equation\\n\\\\(\\\\Delta_{p(x)} u=g+div(\\\\textbf{F})\\\\) are locally Hölder continuous\\nprovided that the functions \\\\(g\\\\) and \\\\(\\\\textbf{F}\\\\) are in suitable\\nLebesgue spaces.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3336/gm.57.1.03\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3336/gm.57.1.03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hölder continuity for the solutions of the p(x)-Laplace equation
with general right-hand side
We show that bounded solutions of the quasilinear elliptic equation
\(\Delta_{p(x)} u=g+div(\textbf{F})\) are locally Hölder continuous
provided that the functions \(g\) and \(\textbf{F}\) are in suitable
Lebesgue spaces.
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