|
|||||
 |
|
|
|
|
|
|
Overdetermined
boundary problems with nonconstant Dirichlet and Neumann
data
Miguel Domínguez-Vázquez, Alberto Enciso and Daniel Peralta-Salas |
|
Vol. 16 (2023), No. 9, 1989–2003
|
 |
Abstract |
|
We consider the overdetermined boundary problem for a general second-order semilinear elliptic equation on bounded domains of , 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. |
Keywords
overdetermined boundary value problems, semilinear elliptic
equations
|
Mathematical Subject Classification
Primary: 35N25
Secondary: 35J61
|
Milestones
Received: 18 August 2020
Revised: 23 March 2022
Accepted: 14 April 2022
Published: 11 November 2023
|
Authors |
| Miguel Domínguez-Vázquez | |
| CITMAga Department of Mathematics Universidade de Santiago de Compostela Spain |
|
| Alberto Enciso | |
| Instituto de Ciencias
Matemáticas Consejo Superior de Investigaciones Científicas Madrid Spain |
|
| Daniel Peralta-Salas | |
| Instituto de Ciencias
Matemáticas Consejo Superior de Investigaciones Científicas Madrid Spain |
|
| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
