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Journal of Convex Analysis 12 (2005), No. 1, 013--044
Copyright Heldermann Verlag 2005

Difference Equations on Weighted Graphs

Alain Bensoussan
Université de Paris-Dauphine, Place du Maréchal Lattre de Tassigny, 75775 Paris, France

José-Luis Menaldi
Wayne State University, Dept. of Mathematics, Detroit, MI 48202, U.S.A.

In discrete systems graphs setting, we mimic the variational formulation of boundary value problems.  Working on with un-normalized weights rather than normalized weights, discrete Dirichlet and Neumann problems, and their probabilistic interpretations are discussed.   Moreover, non-symmetric forms, non-variational setting, and an identification problem are also considered.

Keywords: Connected graphs, connectivity, variational inequalities, discrete maximum principles, Markov chains.

MSC: 05C35, 90C35; 05C40, 35R30, 94C12

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