Concavity of solutions to semilinear equations in dimension two
We consider the Dirichlet problem for a class of semilinear equations on two‐ dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmodem'yanskii. We also prove a result on propag...
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| Veröffentlicht in: | The Bulletin of the London Mathematical Society 2023-04, Vol.55 (2), p.706-716 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We consider the Dirichlet problem for a class of semilinear equations on two‐ dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmodem'yanskii. We also prove a result on propagation of concavity of solutions from the boundary, which holds in all dimensions. |
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| ISSN: | 0024-6093 1469-2120 |
| DOI: | 10.1112/blms.12750 |