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arXiv · 2607.26663

Variational Estimates for Nonnegative Harmonic Functions

Jakob Fromherz
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Abstract

Consider a nonnegative harmonic function $u$ on a domain $D\subset\mathbb{R}^{d-1}$. We establish boundedness of Jones' variational integral on an ultradense, $d-1$ dimensional subset of the boundary of $C^{1,\mathrm{Dini}}$ domains. This result was previously only known for the unit ball.

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Jakob Fromherz. 2026-07-29. Variational Estimates for Nonnegative Harmonic Functions. https://arxiv.org/abs/2607.26663

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