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Discrete Serrin's problem
Arauz Lombardía, Cristina; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. COMPTHE - Combinatòria i Teoria Discreta del Potencial pel control de paràmetres en xarxes
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.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal
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
info:eu-repo/semantics/submittedVersion
Article
Elsevier
         

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