Graphical solutions to one-phase free boundary problems

被引：3
|
作者：
Engelstein, Max [1 ]
Fernandez-Real, Xavier [2 ]
Yu, Hui [3 ]
机构：
[1] Univ Minnesota Twin Cities, Dept Math, 127 Vincent Hall,206 Church St SE, Minneapolis, MN 55455 USA
[2] Ecole Polytech Fed Lausanne, Inst Math, Stn 8, CH-1015 Lausanne, Switzerland
[3] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore
来源：
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2023年 / 2023卷 / 804期
基金：
瑞士国家科学基金会;
关键词：
SEMILINEAR ELLIPTIC-EQUATIONS; FLAT FREE-BOUNDARIES; GLOBAL-SOLUTIONS; REGULARITY; CONJECTURE; INEQUALITY; MINIMIZERS; CONES;
D O I：
10.1515/crelle-2023-0067
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient dimensions, a one-phase free boundary analogue of Bernstein's problem for minimal surfaces. As an application, we also classify monotone solutions of semilinear equations with a bump-type nonlinearity.
引用
收藏
页码：155 / 195
页数：41
相关论文
共 50 条
12345