Alexander P. Sviridov
In a connected finite graph with set of vertices , choose a nonempty subset, not equal to the whole set, , and call it the boundary . Given a real-valued function , our objective is to find a function , such that on , and for all ,
Here are non-negative constants such that , the set is the collection of vertices connected to by an edge, and denotes its cardinality. We prove the existence and uniqueness of a solution of the above Dirichlet problem and study the qualitative properties of the solution.
Submitted October 26, 2010. Published September 6, 2011.
Math Subject Classifications: 35Q91, 35B51, 34A12, 31C20.
Key Words: Dirichlet problem; comparison principle; mean-value property; stochastic games; unique continuation.
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| Alexander P. Sviridov |
Department of Mathematics, University of Pittsburgh
Pittsburgh, PA 15260, USA
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