TY - JOUR
T1 - Graphical solutions to one-phase free boundary problems
AU - Engelstein, Max
AU - Fernández-Real, Xavier
AU - Yu, Hui
N1 - Publisher Copyright:
© De Gruyter 2023.
PY - 2023/11/1
Y1 - 2023/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85175786122&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85175786122&partnerID=8YFLogxK
U2 - 10.1515/crelle-2023-0067
DO - 10.1515/crelle-2023-0067
M3 - Article
AN - SCOPUS:85175786122
SN - 0075-4102
VL - 2023
SP - 155
EP - 195
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 804
ER -