Let $\mathbb{X}$ be a Jordan domain satisfying certain 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 $h$ in [A. Koski, J. Onninen, Sobolev homeomorphic extensions, J. Eur. Math. Soc. 23 (2021) 4065-4089, Theorem 3.1].
Zhuang Wang
,
Haiqing Xu
. IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS*[J]. Acta mathematica scientia, Series B, 2023
, 43(1)
: 373
-386
.
DOI: 10.1007/s10473-023-0121-8
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