Higher integrability of the gradient for the thermal insulation problem

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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