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arXiv · 2104.07873

Improved regularity of harmonic diffeomorphic extensions on quasihyperbolic domains

Zhuang Wang·Haiqing Xu
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Abstract

Let $\mathbb{X}$ be a Jordan domain satisfying hyperbolic growth conditions. Assume that $\varphi$ is a homeomorphism from the boundary $\partial \mathbb{X}$ of $\mathbb{X}$ onto the unit circle. Denote by $h$ the harmonic diffeomorphic extension of $\varphi $ from $\mathbb{X}$ onto the unit disk. We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of $h.$ These generalize the Sobolev regularity of $h$ by Koski-Onninen [21, Theorem 3.1].

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Zhuang Wang, Haiqing Xu. 2021-04-16. Improved regularity of harmonic diffeomorphic extensions on quasihyperbolic domains. https://arxiv.org/abs/2104.07873

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