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

页码：155 / 195

页数：41

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