Bibliographic Details
| Title: |
Dirichlet problem on locally finite graphs |
| Authors: |
Javaheri, Mohammad1 javaheri@uoregon.edu |
| Source: |
Discrete Applied Mathematics. Nov2007, Vol. 155 Issue 18, p2496-2506. 11p. |
| Subjects: |
Dirichlet problem, Boundary value problems, Parabolic differential equations, Mathematics |
| Abstract: |
Abstract: In this paper, we study the existence and uniqueness of solutions to the vertex-weighted Dirichlet problem on locally finite graphs. Let B be a subset of the vertices of a graph G. The Dirichlet problem is to find a function whose discrete Laplacian on and its values on B are given. Each infinite connected component of is called an end of G relative to B. If there are no ends, then there is a unique solution to the Dirichlet problem. Such a solution can be obtained as a limit of an averaging process or as a minimizer of a certain functional or as a limit-solution of the heat equation on the graph. On the other hand, we show that if G is a locally finite graph with l ends, then the set of solutions of any Dirichlet problem, if non-empty, is at least l-dimensional. [Copyright &y& Elsevier] |
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| Database: |
Engineering Source |
