{"title":"利用Wolff势对加权抛物型p-拉普拉斯方程解的点态估计","authors":"Yevhen Zozulia","doi":"10.37069/1683-4720-2022-36-07","DOIUrl":null,"url":null,"abstract":"For the weighted parabolic equation \\v\\left(x \\right)u_{t} -{\\hbox{div}({w(x)| \\nabla u |^{p-2}}} \\nabla u) = f , p >{2} we prove the local boundedness for weak solutions in terms of the weighted Wolff potential of the right-hand side of equation.","PeriodicalId":484640,"journal":{"name":"Trudy Instituta prikladnoj matematiki i mehaniki","volume":"33 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pointwise estimates of solutions to weighted parabolic p-Laplacian equation via Wolff potential\",\"authors\":\"Yevhen Zozulia\",\"doi\":\"10.37069/1683-4720-2022-36-07\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For the weighted parabolic equation \\\\v\\\\left(x \\\\right)u_{t} -{\\\\hbox{div}({w(x)| \\\\nabla u |^{p-2}}} \\\\nabla u) = f , p >{2} we prove the local boundedness for weak solutions in terms of the weighted Wolff potential of the right-hand side of equation.\",\"PeriodicalId\":484640,\"journal\":{\"name\":\"Trudy Instituta prikladnoj matematiki i mehaniki\",\"volume\":\"33 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-02-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Trudy Instituta prikladnoj matematiki i mehaniki\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37069/1683-4720-2022-36-07\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Trudy Instituta prikladnoj matematiki i mehaniki","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37069/1683-4720-2022-36-07","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
对于加权抛物方程\v\left (x \right){u＿t} - {\hbox{div} (w(x)|{\nabla u |^p{-2}}}\nabla u) = f, p ＆gt;{2}，用方程右侧的加权Wolff势证明了弱解的局部有界性。
Pointwise estimates of solutions to weighted parabolic p-Laplacian equation via Wolff potential
For the weighted parabolic equation \v\left(x \right)u_{t} -{\hbox{div}({w(x)| \nabla u |^{p-2}}} \nabla u) = f , p >{2} we prove the local boundedness for weak solutions in terms of the weighted Wolff potential of the right-hand side of equation.
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