{"title":"具有一般核的非局部时间亚扩散方程的荷尔德正则性","authors":"Adam Kubica, Katarzyna Ryszewska, Rico Zacher","doi":"arxiv-2409.04841","DOIUrl":null,"url":null,"abstract":"We study the regularity of weak solutions to nonlocal in time subdiffusion\nequations for a wide class of weakly singular kernels appearing in the\ngeneralised fractional derivative operator. We prove a weak Harnack inequality\nfor nonnegative weak supersolutions and Holder continuity of weak solutions to\nsuch problems. Our results substantially extend the results from our previous\nwork [12] by leaving the framework of distributed order fractional time\nderivatives and considering a general PC kernel and by also allowing for an\ninhomogeneity in the PDE from a Lebesgue space of mixed type.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"6 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Holder regularity for nonlocal in time subdiffusion equations with general kernel\",\"authors\":\"Adam Kubica, Katarzyna Ryszewska, Rico Zacher\",\"doi\":\"arxiv-2409.04841\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the regularity of weak solutions to nonlocal in time subdiffusion\\nequations for a wide class of weakly singular kernels appearing in the\\ngeneralised fractional derivative operator. We prove a weak Harnack inequality\\nfor nonnegative weak supersolutions and Holder continuity of weak solutions to\\nsuch problems. Our results substantially extend the results from our previous\\nwork [12] by leaving the framework of distributed order fractional time\\nderivatives and considering a general PC kernel and by also allowing for an\\ninhomogeneity in the PDE from a Lebesgue space of mixed type.\",\"PeriodicalId\":501165,\"journal\":{\"name\":\"arXiv - MATH - Analysis of PDEs\",\"volume\":\"6 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Analysis of PDEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.04841\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04841","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们研究了广义分数导数算子中出现的一大类弱奇异核的非局部时间亚扩散方程弱解的正则性。我们证明了非负弱超解的弱哈纳克不等式以及此类问题弱解的连续性。通过离开分布阶分数时间导数的框架并考虑一般 PC 核,以及通过允许来自混合类型的 Lebesgue 空间的 PDE 中的非均质性,我们的结果大大扩展了我们之前的工作[12]。
Holder regularity for nonlocal in time subdiffusion equations with general kernel
We study the regularity of weak solutions to nonlocal in time subdiffusion
equations for a wide class of weakly singular kernels appearing in the
generalised fractional derivative operator. We prove a weak Harnack inequality
for nonnegative weak supersolutions and Holder continuity of weak solutions to
such problems. Our results substantially extend the results from our previous
work [12] by leaving the framework of distributed order fractional time
derivatives and considering a general PC kernel and by also allowing for an
inhomogeneity in the PDE from a Lebesgue space of mixed type.