Graphical solutions to one-phase free boundary problems
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.
WOS:001089069400001
2023-10-27
2023
804
155
195
REVIEWED
EPFL
Funder | Grant Number |
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) | |