具有缓慢增长和低阶项的能量积分的局部 Lipschitz 连续性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2024-10-03 DOI:10.1016/j.nonrwa.2024.104224

Michela Eleuteri , Stefania Perrotta , Giulia Treu

{"title":"具有缓慢增长和低阶项的能量积分的局部 Lipschitz 连续性","authors":"Michela Eleuteri , Stefania Perrotta , Giulia Treu","doi":"10.1016/j.nonrwa.2024.104224","DOIUrl":null,"url":null,"abstract":"<div><div>We consider integral functionals with slow growth and explicit dependence on <span><math><mi>u</mi></math></span> of the Lagrangian; this includes many relevant examples as, for instance, in elastoplastic torsion problems or in image restoration problems. Our aim is to prove that the local minimizers are locally Lipschitz continuous. The proof makes use of recent results concerning the Bounded Slope Conditions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"82 ","pages":"Article 104224"},"PeriodicalIF":1.8000,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local Lipschitz continuity for energy integrals with slow growth and lower order terms\",\"authors\":\"Michela Eleuteri , Stefania Perrotta , Giulia Treu\",\"doi\":\"10.1016/j.nonrwa.2024.104224\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We consider integral functionals with slow growth and explicit dependence on <span><math><mi>u</mi></math></span> of the Lagrangian; this includes many relevant examples as, for instance, in elastoplastic torsion problems or in image restoration problems. Our aim is to prove that the local minimizers are locally Lipschitz continuous. The proof makes use of recent results concerning the Bounded Slope Conditions.</div></div>\",\"PeriodicalId\":49745,\"journal\":{\"name\":\"Nonlinear Analysis-Real World Applications\",\"volume\":\"82 \",\"pages\":\"Article 104224\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-10-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Real World Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1468121824001639\",\"RegionNum\":3,\"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":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824001639","RegionNum":3,"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

我们考虑的是增长缓慢且明确依赖于拉格朗日 u 的积分函数；这包括许多相关的例子，例如弹塑性扭转问题或图像复原问题。我们的目的是证明局部最小值是局部 Lipschitz 连续的。该证明利用了有关有界斜率条件的最新成果。

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

Local Lipschitz continuity for energy integrals with slow growth and lower order terms

We consider integral functionals with slow growth and explicit dependence on

u

of the Lagrangian; this includes many relevant examples as, for instance, in elastoplastic torsion problems or in image restoration problems. Our aim is to prove that the local minimizers are locally Lipschitz continuous. The proof makes use of recent results concerning the Bounded Slope Conditions.

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-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.