A free boundary problem related to thermal insulation

被引：25

作者：

Caffarelli, Luis A. ^{[1
]}

Kriventsov, Dennis ^{[2
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2016年 / 41卷 / 07期

基金：

美国国家科学基金会;

关键词：

Free boundary; free discontinuity; insulation; Robin; MINIMUM PROBLEM; REGULARITY; MONOTONICITY; EXISTENCE;

D O I：

10.1080/03605302.2016.1199038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but rather a hypersurface along which a harmonic function satisfies a Robin condition. We show that minimal sets exist, satisfy uniform density estimates, and, under some geometric conditions, have "locally flat" boundaries.

引用

页码：1149 / 1182

页数：34

共 18 条

[1]

Aguilera NE., 1987, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), V14, P355

[2]

ALT HW, 1981, J REINE ANGEW MATH, V325, P105

[3]

Ambrosio L., 2000, Oxford Mathematical Monographs

[4]

[Anonymous], 1960, Arch. Math. (Basel)

[5]

Bonnet A, 1996, PROG NONLIN, V25, P93

[6]

Bucur D., SYMMETRY BREAKING PR

[7]

Bucur D., ANN I H POI IN PRESS

[8] Monotonicity Formula and Regularity for General Free Discontinuity Problems [J].

Bucur, Dorin ;

Luckhaus, Stephan .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 211 (02) :489-511

[9] Monotonicity and separation for the Mumford-Shah problem [J].

David, G ;

Léger, JC .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2002, 19 (05) :631-682

[10]

David G, 1993, Mathematical Surveys and Monographs, V38

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