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Potential Theory for boundary value problems on finite networks
Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gesto Beiroa, José Manuel
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. VARIDIS - Varietats Riemannianes Discretes i Teoria del Potencial
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.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta
Potential theory (Mathematics)
Boundary value problems
Schrödinger operator
Green's functions
Discrete Potential Theory
Combinatorial Laplacian
Schrödinger operator
Boundary value problems
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}
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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