Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities
We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on R and on compact Riemannian manifolds. As a byproduct of the proofs we also obtain some rigidity, or partial symmet...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:dnet:digitalcsic_::26aacc1e75ef0fdad9f4066907435037 |
| Acceso en línea: | http://hdl.handle.net/10261/195687 |
| Access Level: | acceso abierto |
| Palabra clave: | Semilinear elliptic problems Symmetric spaces Asymptotically homogeneous spaces Harmonic spaces Overdetermined boundary value problems |
| Sumario: | We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on R and on compact Riemannian manifolds. As a byproduct of the proofs we also obtain some rigidity, or partial symmetry, results for solutions to overdetermined problems on Riemannian manifolds of nonconstant curvature. |
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