OVERDETERMINED BOUNDARY PROBLEMS WITH NONCONSTANT DIRICHLET AND NEUMANN DATA
We consider the overdetermined boundary problem for a general second-order semilinear elliptic equation on bounded domains of Rn, where one prescribes both the Dirichlet and Neumann data of the solution. We are interested in the case where the data are not necessarily constant and where the coeffici...
| Autores: | , , |
|---|---|
| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/348127 |
| Acesso em linha: | http://hdl.handle.net/10261/348127 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85178405741&doi=10.2140%2fapde.2023.16.1989&partnerID=40&md5=bed42be681d00e80b60252013e755eab |
| Access Level: | acceso abierto |
| Palavra-chave: | Overdetermined boundary value problems Semilinear elliptic equations |
| Resumo: | We consider the overdetermined boundary problem for a general second-order semilinear elliptic equation on bounded domains of Rn, where one prescribes both the Dirichlet and Neumann data of the solution. We are interested in the case where the data are not necessarily constant and where the coefficients of the equation can depend on the position, so that the overdetermined problem does not generally admit a radial solution. Our main result is that, nevertheless, under minor technical hypotheses nontrivial solutions to the overdetermined boundary problem always exist. © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open. All Rights Reserved. |
|---|