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Creators/Authors contains: "Fernández-Real, Xavier"

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  1. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    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. 
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