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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 155-195 |
| Number of pages | 41 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Volume | 2023 |
| Issue number | 804 |
| DOIs | |
| State | Published - Nov 1 2023 |
Bibliographical note
Publisher Copyright:© De Gruyter 2023.
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