The Strong Maximum Principle on Infinite Networks
نویسنده
چکیده
We study the strong maximum principle for the heat equation associated with the Dirichlet form on an infinite network. We prove that the strong maximum principle is equivalent to the underlying graph being connected after deletion of the nodes with infinite degree. Using this result, we prove that the multiplicity of the eigenvalue 0 of a generalization of the Laplace matrix equals the number of connected components of the graph with respect to the heat flow.
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