Graphical solutions to one-phase free boundary problems
2023
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.
Details
Title
Graphical solutions to one-phase free boundary problems
Author(s)
Engelstein, Max ; Fernandez-Real, Xavier ; Yu, Hui
Published in
Journal Fur Die Reine Und Angewandte Mathematik
Volume
2023
Issue
804
Pages
155-195
Date
2023-10-27
Publisher
Walter De Gruyter Gmbh, Berlin
ISSN
0075-4102
1435-5345
1435-5345
Keywords
Other identifier(s)
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Laboratories
AMCV
Record Appears in
Scientific production and competences > SB - School of Basic Sciences > MATH - Institute of Mathematics > AMCV - Chair of Mathematical Analysis, Calculus of Variations and PDEs
Peer-reviewed publications
Work produced at EPFL
Journal Articles
Published
Peer-reviewed publications
Work produced at EPFL
Journal Articles
Published
Grant
NSF: DMS 2000288
NSF CAREER: 2143719
Swiss National Science Foundation (SNF): 200021_182565
Swiss State Secretariat for Education, Research and lnnovation (SERI): MB22.00034
AEI project: PID2021-125021NAI00
Presidential Young Professor Fund (National University of Singapore)
NSF CAREER: 2143719
Swiss National Science Foundation (SNF): 200021_182565
Swiss State Secretariat for Education, Research and lnnovation (SERI): MB22.00034
AEI project: PID2021-125021NAI00
Presidential Young Professor Fund (National University of Singapore)
Record creation date
2024-02-16