Discrete Serrin's problem
We consider here the discrete analogue of Serrin's problem: if the equilibrium measure of a network with boundary satisfies that its normal derivative is constant, what can be said about the structure of the network and the symmetry of the equilibrium measure? In the original Serrin's prob...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/27649 |
| Acesso em linha: | https://hdl.handle.net/2117/27649 https://dx.doi.org/10.1016/j.laa.2014.01.038 |
| Access Level: | acceso abierto |
| Palavra-chave: | Serrin's problem Overdetermined boundary value problems Equilibrium measure Spider networks Minimum principle BOUNDARY-VALUE-PROBLEMS POTENTIAL-THEORY SYMMETRY PROBLEM EQUATIONS NETWORKS Problema de Serrin Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal |
| Resumo: | We consider here the discrete analogue of Serrin's problem: if the equilibrium measure of a network with boundary satisfies that its normal derivative is constant, what can be said about the structure of the network and the symmetry of the equilibrium measure? In the original Serrin's problem, the conclusion is that the domain is a ball and the solution is radial. To study the discrete Serrin's problem, we first introduce the notion of radial function and then prove a generalization of the minimum principle, which is one of the main tools in the continuous case. Moreover, we obtain similar results to those of the continuous case for some families of networks with a ball-like structure, which include spider networks with radial conductances, distance-regular graphs or, more generally, regular layered networks. |
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