Graphical solutions to one-phase free boundary problems-Reference-Cited by-同舟云学术

Graphical solutions to one-phase free boundary problems

Published:2023-10-27 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Engelstein Max¹,Fernández-Real Xavier²,Yu Hui³

Affiliation:

1. Department of Mathematics , University of Minnesota Twin Cities , 127 Vincent Hall, 206 Church St., SE Minneapolis , MN 55455 , USA

2. Institute of Mathematics , EPFL , SB, Station 8, CH-1015 Lausanne , Switzerland

3. Department of Mathematics , National University of Singapore , Singapore 119076 , Singapore

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2023-0067/pdf

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