{"title":"关于进化分数阶p-拉普拉斯算子","authors":"Dimitri Puhst","doi":"10.1093/AMRX/ABV003","DOIUrl":null,"url":null,"abstract":"In this work existence results on nonlinear first order as well as doubly nonlinear second order evolution equations involving the fractional p-Laplacian are presented. The proofs do not exploit any monotonicity assumption but rely on a compactness argument in combination with regularity of the Galerkin scheme and the nonlocal character of the operator.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"72 1","pages":"253-273"},"PeriodicalIF":0.0000,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"42","resultStr":"{\"title\":\"On the Evolutionary Fractional p-Laplacian\",\"authors\":\"Dimitri Puhst\",\"doi\":\"10.1093/AMRX/ABV003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work existence results on nonlinear first order as well as doubly nonlinear second order evolution equations involving the fractional p-Laplacian are presented. The proofs do not exploit any monotonicity assumption but rely on a compactness argument in combination with regularity of the Galerkin scheme and the nonlocal character of the operator.\",\"PeriodicalId\":89656,\"journal\":{\"name\":\"Applied mathematics research express : AMRX\",\"volume\":\"72 1\",\"pages\":\"253-273\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"42\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied mathematics research express : AMRX\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/AMRX/ABV003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied mathematics research express : AMRX","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/AMRX/ABV003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this work existence results on nonlinear first order as well as doubly nonlinear second order evolution equations involving the fractional p-Laplacian are presented. The proofs do not exploit any monotonicity assumption but rely on a compactness argument in combination with regularity of the Galerkin scheme and the nonlocal character of the operator.
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