Sobolev homeomorphic extensions from two to three dimensions
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Journal of Functional Analysis, Volume 286, issue 9
Abstract
We study the basic question of characterizing which boundary homeomorphisms of the unit sphere can be extended to a Sobolev homeomorphism of the interior in 3D space. While the planar variants of this problem are well-understood, completely new and direct ways of constructing an extension are required in 3D. We prove, among other things, that a Sobolev homeomorphism φ:R2→ontoR2 in Wloc1,p(R2,R2) for some p∈[1,∞) admits a homeomorphic extension h:R3→ontoR3 in Wloc1,q(R3,R3) for [Formula presented]. Such an extension result is nearly sharp, as the bound [Formula presented] cannot be improved due to the Hölder embedding. The case q=3 gains an additional interest as it also provides an L1-variant of the celebrated Beurling-Ahlfors quasiconformal extension result.Description
| openaire: EC/H2020/834728/EU//QUAMAP
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Hencl, S, Koski, A & Onninen, J 2024, 'Sobolev homeomorphic extensions from two to three dimensions', Journal of Functional Analysis, vol. 286, no. 9, 110371. https://doi.org/10.1016/j.jfa.2024.110371