On a free boundary problem and minimal surfaces

被引：1

作者：

Liu, Yong ^{[1
]}

Wang, Kelei ^{[2
]}

Wei, Juncheng ^{[3
]}

机构：

[1] North China Elect Power Univ, Sch Math & Phys, Beijing, Peoples R China

[2] Wuhan Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China

[3] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2018年 / 35卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Free boundary problems; Minimal surfaces; Global minimizers; Allen-Cahn equation; Reduction method; ALLEN-CAHN EQUATION; ELLIPTIC PDES; REGULARITY; CONJECTURE; CURVATURE; STABILITY; CONES;

D O I：

10.1016/j.anihpc.2017.09.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov-Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension 8, using variational arguments, we also obtain solutions which are global minimizers of the corresponding energy functional. This shows that the theorem of Valdinoci et al. [41,42] is optimal. (C) 2017 Elsevier Masson SAS. All rights reserved.

引用

页码：993 / 1017

页数：25

共 44 条

[1] Higher-Dimensional Catenoid, Liouville Equation, and Allen-Cahn Equation [J].

Agudelo, Oscar ;

del Pino, Manuel ;

Wei, Juncheng .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016, 2016 (23) :7051-7102

[2]

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

[3] VARIATIONAL-PROBLEMS WITH 2 PHASES AND THEIR FREE BOUNDARIES [J].

ALT, HW ;

CAFFARELLI, LA ;

FRIEDMAN, A .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 282 (02) :431-461

[4] Entire solutions of semilinear elliptic equations in R3 and a conjecture of De Giorgi [J].

Ambrosio, L ;

Cabré, X .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 13 (04) :725-739

[5] MINIMAL CONES AND BERNSTEIN PROBLEM [J].

BOMBIERI, E ;

DEGIORGI, E ;

GIUSTI, E .

INVENTIONES MATHEMATICAE, 1969, 7 (03) :243-&

[6]

Caffarelli L.A., 1987, Rev. Mat. Iberoamericana, V3, P139

[7] A HARNACK INEQUALITY APPROACH TO THE REGULARITY OF FREE BOUNDARIES .2. FLAT FREE BOUNDARIES ARE LIPSCHITZ [J].

CAFFARELLI, LA .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (01) :55-78

[8]

Caffarelli LA, 2004, CONTEMP MATH, V353, P43

[9]

Caffarelli LuisA., 1989, Ann. Scuola Norm. Sup. Pisa Cl. Sci, V15, P583

[10] A Gradient Bound for Free Boundary Graphs [J].

De Silva, Daniela ;

Jerison, David .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2011, 64 (04) :538-555

← 1 2 3 4 5 →