Sobolev homeomorphic extensions onto John domains
Koskela, P., Koski, A., & Onninen, J. (2020). Sobolev homeomorphic extensions onto John domains. Journal of Functional Analysis, 279(10), Article 108719. https://doi.org/10.1016/j.jfa.2020.108719
Published inJournal of Functional Analysis
DisciplineAnalyysin ja dynamiikan tutkimuksen huippuyksikköMatematiikkaAnalysis and Dynamics Research (Centre of Excellence)Mathematics
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© 2020 Elsevier
Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schöenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous W1,2-extension but not even a homeomorphic W1,1-extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents p<2. John disks, being one sided quasidisks, are of fundamental importance in Geometric Function Theory.
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Related funder(s)European Commission; Academy of Finland
Funding program(s)FP7 (EU's 7th Framework Programme); Academy Project, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingP. Koskela was supported by the Academy of Finland Grant number 323960. A. Koski was supported by the Academy of Finland Grant number 307023. J. Onninen was supported by the NSF grant DMS-1700274.
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