Engelstein, MaxFernandez-Real, XavierYu, Hui2024-02-162024-02-162024-02-162023-10-2710.1515/crelle-2023-0067https://infoscience.epfl.ch/handle/20.500.14299/203939WOS:001089069400001We 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.Physical SciencesSemilinear Elliptic-EquationsFlat Free-BoundariesGlobal-SolutionsRegularityConjectureInequalityMinimizersConestext::journal::journal article::research article