After the Explosion: Dirichlet Forms and Boundary Problems for Infinite Graphs

Details After the Explosion: Dirichlet Forms and Boundary Problems for Infinite Graphs After the Explosion: Dirichlet Forms and Boundary Problems for Infinite Graphs

2011-09-14

arxiv.org/abs/1109.3137v1

Mathematics

Functional Analysis

Scientific paper

Formal Laplace operators are analyzed for a large class of resistance networks with vertex weights. The graphs are completed with respect to the minimal resistance path metric. Compactness and a novel connectivity hypothesis for the completed graphs play an essential role. A version of the Dirichlet problem is solved. Self adjoint Laplace operators and the probability semigroups they generate are constructed using reflecting and absorbing conditions on subsets of the graph boundary.

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