Potential Theory for boundary value problems on finite networks
We aim here at analyzing self-adjoint boundary value problems on finite networks associated with positive semi-definite Schrödinger operators. In addition, we study the existence and uniqueness of solutions and its variational formulation. Moreover, we will tackle a well-known problem in the framewo...
| Autores: | , , , |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 2006 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/589 |
| Acesso em linha: | https://hdl.handle.net/2117/589 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Potential theory (Mathematics) Boundary value problems Schrödinger operator Green's functions Discrete Potential Theory Combinatorial Laplacian Schrödinger operator Effective resistance Green function Potencial, Teoria del (Matemàtica) Problemes extrems (Matemàtica) Xarxes de comunicacions Classificació AMS::34 Ordinary differential equations::34B Boundary value problems {For ordinary differential operators, see 34Lxx} Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta |
| Resumo: | We aim here at analyzing self-adjoint boundary value problems on finite networks associated with positive semi-definite Schrödinger operators. In addition, we study the existence and uniqueness of solutions and its variational formulation. Moreover, we will tackle a well-known problem in the framework of Potential Theory, the so-called condenser principle. Then, we generalize of the concept of effective resistance between two vertices of the network and we characterize the Green function of some BVP in terms of effective resistances. |
|---|