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...

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Detalles Bibliográficos
Autores: Domínguez-Vázquez, M., Enciso, A., Peralta-Salas, D.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/348127
Acceso en línea: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
Palabra clave:Overdetermined boundary value problems
Semilinear elliptic equations
Descripción
Sumario: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.