학술
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Variational Estimates for Nonnegative Harmonic Functions
arXiv Math
CC BY
이 매체는 공공·자유 라이선스로 본문을 직접 표시합니다.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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