一类完全非线性双散度系统的两相自由边界问题

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-09-03 DOI:10.1016/j.na.2025.113936

Pêdra D.S. Andrade , Julio C. Correa

{"title":"一类完全非线性双散度系统的两相自由边界问题","authors":"Pêdra D.S. Andrade , Julio C. Correa","doi":"10.1016/j.na.2025.113936","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, we study a class of fully nonlinear double-divergence systems with free boundaries associated with a minimization problem. The variational structure of the Hessian-dependent functional plays a fundamental role in proving the existence of the minimizers and then the existence of the solutions for the system. In addition, we establish improvements in integrability for the equation in the double-divergence form. Consequently, we improve the regularity for the fully nonlinear equation in Sobolev and Hölder spaces.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113936"},"PeriodicalIF":1.3000,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two-phase free boundary problems for a class of fully nonlinear double-divergence systems\",\"authors\":\"Pêdra D.S. Andrade , Julio C. Correa\",\"doi\":\"10.1016/j.na.2025.113936\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this article, we study a class of fully nonlinear double-divergence systems with free boundaries associated with a minimization problem. The variational structure of the Hessian-dependent functional plays a fundamental role in proving the existence of the minimizers and then the existence of the solutions for the system. In addition, we establish improvements in integrability for the equation in the double-divergence form. Consequently, we improve the regularity for the fully nonlinear equation in Sobolev and Hölder spaces.</div></div>\",\"PeriodicalId\":49749,\"journal\":{\"name\":\"Nonlinear Analysis-Theory Methods & Applications\",\"volume\":\"262 \",\"pages\":\"Article 113936\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2025-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Theory Methods & Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0362546X25001889\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X25001889","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了一类具有自由边界的完全非线性双散度系统的最小化问题。Hessian-dependent泛函的变分结构在证明系统极小值的存在性和解的存在性方面起着重要的作用。此外，我们建立了双散度形式方程可积性的改进。因此，我们改进了Sobolev和Hölder空间中全非线性方程的正则性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Two-phase free boundary problems for a class of fully nonlinear double-divergence systems

In this article, we study a class of fully nonlinear double-divergence systems with free boundaries associated with a minimization problem. The variational structure of the Hessian-dependent functional plays a fundamental role in proving the existence of the minimizers and then the existence of the solutions for the system. In addition, we establish improvements in integrability for the equation in the double-divergence form. Consequently, we improve the regularity for the fully nonlinear equation in Sobolev and Hölder spaces.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.