Monotonicity formulas for harmonic functions on the infinite regular tree
Abstract
We continue the program initiated in SVGS. In this paper, we focus on the infinite d-regular tree, and prove the monotonicity of a weighted Dirichlet energy, a Weiss-type monotonicity formula, and a generalization of the Almgren monotonicity formula of SVGS for p 1. We also compute examples in the infinite 2- and 3-regular trees.
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