{"title":"[公式省略]域上完全非线性抛物不等式的估计","authors":"Xuemei Li","doi":"10.1016/j.aml.2025.109459","DOIUrl":null,"url":null,"abstract":"In this paper, we study boundary <mml:math altimg=\"si4.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msup></mml:math> estimates for solution sets of fully nonlinear parabolic inequalities <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">−</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"script\">M</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:mi>Λ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">≤</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">≤</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">−</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"script\">M</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:mi>Λ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> on <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi></mml:mrow></mml:msup></mml:math> domains, which generalize results for elliptic equations in Li and Li (2023).","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"23 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"[formula omitted] estimates for fully nonlinear parabolic inequalities on [formula omitted] domains\",\"authors\":\"Xuemei Li\",\"doi\":\"10.1016/j.aml.2025.109459\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study boundary <mml:math altimg=\\\"si4.svg\\\" display=\\\"inline\\\"><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msup></mml:math> estimates for solution sets of fully nonlinear parabolic inequalities <mml:math altimg=\\\"si2.svg\\\" display=\\\"inline\\\"><mml:mrow><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo linebreak=\\\"goodbreak\\\" linebreakstyle=\\\"after\\\">−</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\\\"script\\\">M</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:mi>Λ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo linebreak=\\\"goodbreak\\\" linebreakstyle=\\\"after\\\">≤</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo linebreak=\\\"goodbreak\\\" linebreakstyle=\\\"after\\\">≤</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo linebreak=\\\"goodbreak\\\" linebreakstyle=\\\"after\\\">−</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\\\"script\\\">M</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:mi>Λ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> on <mml:math altimg=\\\"si5.svg\\\" display=\\\"inline\\\"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi></mml:mrow></mml:msup></mml:math> domains, which generalize results for elliptic equations in Li and Li (2023).\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"23 1\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2025-01-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1016/j.aml.2025.109459\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.aml.2025.109459","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了全非线性抛物不等式 ut-M+(D2u,λ,Λ)≤f(x,t)≤ut-M-(D2u,λ,Λ) 在 C1,α 域上的解集的边界 W2,δ 估计，它概括了 Li 和 Li (2023) 中关于椭圆方程的结果。
[formula omitted] estimates for fully nonlinear parabolic inequalities on [formula omitted] domains
In this paper, we study boundary W2,δ estimates for solution sets of fully nonlinear parabolic inequalities ut−M+(D2u,λ,Λ)≤f(x,t)≤ut−M−(D2u,λ,Λ) on C1,α domains, which generalize results for elliptic equations in Li and Li (2023).
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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