Higher integrability of the gradient for the thermal insulation problem

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries Pub Date : 2021-01-24 DOI:10.4171/ifb/481

Camille Labourie, Emmanouil Milakis

引用次数: 2

Abstract

We prove the higher integrability of the gradient for local minimizers of the thermal insulation problem, an analogue of De Giorgi’s conjecture for the Mumford-Shah functional. We deduce that the singular part of the free boundary has Hausdorff dimension strictly less than n− 1. AMS Subject Classifications: 35R35, 35J20, 49N60, 49Q20.

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绝热问题中梯度的高可积性

我们证明了绝热问题的梯度的高可积性，这是对Mumford-Shah泛函的De Giorgi猜想的一个类似。我们推导出自由边界奇异部分的Hausdorff维数严格小于n - 1。AMS学科分类:35R35、35J20、49N60、49Q20。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Interfaces and Free Boundaries 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.