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Discrete Serrin's problem

Author
Arauz, C.; Carmona, A.; Encinas, A.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2015-03-01
Volume
468
First page
107
Last page
121
DOI
https://doi.org/10.1016/j.laa.2014.01.038 Open in new window
Project funding
Problemas de contorno discretos y técnicas de aproximación en estados de equilibrio
Repository
http://hdl.handle.net/2117/27649 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S002437951400072X Open in new window
Abstract
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 minim...
Citation
Arauz, C.; Carmona, A.; Encinas, A. Discrete Serrin's problem. "Linear algebra and its applications", 01 Març 2015, vol. 468, p. 107-121.
Keywords
BOUNDARY-VALUE-PROBLEMS, EQUATIONS, Equilibrium measure, Minimum principle, NETWORKS, Overdetermined boundary value problems, POTENTIAL-THEORY, SYMMETRY PROBLEM, Serrin's problem, Spider networks
Group of research
MAPTHE - Matrix Analysis and Discrete Potential Theory

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