Academic paper
Variational Estimates for Nonnegative Harmonic Functions
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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