Journal of Convex Analysis 12 (2005), No. 1, 013--044
Copyright Heldermann Verlag 2005
Difference Equations on Weighted Graphs
Université de Paris-Dauphine, Place du Maréchal Lattre de Tassigny, 75775 Paris, France
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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