{"title":"双非线性分数 p-Laplacian 方程的存在性","authors":"Nobuyuki Kato, Masashi Misawa, Kenta Nakamura, Yoshihiko Yamaura","doi":"10.1007/s10231-024-01453-z","DOIUrl":null,"url":null,"abstract":"<div><p>We prove the existence of a global-in-time weak solution to a doubly nonlinear parabolic fractional <i>p</i>-Laplacian equation, which has general double nonlinearity including not only the Sobolev subcritical/critical/supercritical cases but also the slow/homogenous/fast diffusion ones. Our proof exploits the weak convergence method for the doubly nonlinear fractional <i>p</i>-Laplace operator.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence for doubly nonlinear fractional p-Laplacian equations\",\"authors\":\"Nobuyuki Kato, Masashi Misawa, Kenta Nakamura, Yoshihiko Yamaura\",\"doi\":\"10.1007/s10231-024-01453-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove the existence of a global-in-time weak solution to a doubly nonlinear parabolic fractional <i>p</i>-Laplacian equation, which has general double nonlinearity including not only the Sobolev subcritical/critical/supercritical cases but also the slow/homogenous/fast diffusion ones. Our proof exploits the weak convergence method for the doubly nonlinear fractional <i>p</i>-Laplace operator.</p></div>\",\"PeriodicalId\":8265,\"journal\":{\"name\":\"Annali di Matematica Pura ed Applicata\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali di Matematica Pura ed Applicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10231-024-01453-z\",\"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":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10231-024-01453-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Existence for doubly nonlinear fractional p-Laplacian equations
We prove the existence of a global-in-time weak solution to a doubly nonlinear parabolic fractional p-Laplacian equation, which has general double nonlinearity including not only the Sobolev subcritical/critical/supercritical cases but also the slow/homogenous/fast diffusion ones. Our proof exploits the weak convergence method for the doubly nonlinear fractional p-Laplace operator.
期刊介绍：
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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