{"title":"奇异抛物线双相系统的梯度高积分性","authors":"","doi":"10.1007/s00030-024-00928-5","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We prove a local higher integrability result for the gradient of a weak solution to parabolic double-phase systems of <em>p</em>-Laplace type when <span> <span>\\(\\tfrac{2n}{n+2}< p\\le 2\\)</span> </span>. The result is based on a reverse Hölder inequality in intrinsic cylinders combining <em>p</em>-intrinsic and (<em>p</em>, <em>q</em>)-intrinsic geometries. A singular scaling deficits affects the range of <em>q</em>.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"41 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gradient higher integrability for singular parabolic double-phase systems\",\"authors\":\"\",\"doi\":\"10.1007/s00030-024-00928-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> <p>We prove a local higher integrability result for the gradient of a weak solution to parabolic double-phase systems of <em>p</em>-Laplace type when <span> <span>\\\\(\\\\tfrac{2n}{n+2}< p\\\\le 2\\\\)</span> </span>. The result is based on a reverse Hölder inequality in intrinsic cylinders combining <em>p</em>-intrinsic and (<em>p</em>, <em>q</em>)-intrinsic geometries. A singular scaling deficits affects the range of <em>q</em>.</p>\",\"PeriodicalId\":501665,\"journal\":{\"name\":\"Nonlinear Differential Equations and Applications (NoDEA)\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Differential Equations and Applications (NoDEA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00030-024-00928-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Differential Equations and Applications (NoDEA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00030-024-00928-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Gradient higher integrability for singular parabolic double-phase systems
Abstract
We prove a local higher integrability result for the gradient of a weak solution to parabolic double-phase systems of p-Laplace type when \(\tfrac{2n}{n+2}< p\le 2\). The result is based on a reverse Hölder inequality in intrinsic cylinders combining p-intrinsic and (p, q)-intrinsic geometries. A singular scaling deficits affects the range of q.
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