Monotonicity formulas for harmonic functions on the infinite regular tree
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910051920248832 |
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| author | Atwood, Kathryn Garcia, Mariana Smit Vega Wang, Richard |
| author_facet | Atwood, Kathryn Garcia, Mariana Smit Vega Wang, Richard |
| contents | We continue the program initiated in \cite{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 \cite{SVGS} for $p\ge 1$. We also compute examples in the infinite $2-$ and $3-$regular trees. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_13132 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monotonicity formulas for harmonic functions on the infinite regular tree Atwood, Kathryn Garcia, Mariana Smit Vega Wang, Richard Analysis of PDEs We continue the program initiated in \cite{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 \cite{SVGS} for $p\ge 1$. We also compute examples in the infinite $2-$ and $3-$regular trees. |
| title | Monotonicity formulas for harmonic functions on the infinite regular tree |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.13132 |