Abstract
We give conditions on k, p and the dimension of the space characterizing when the Lusin (N) condition holds in \(W^{k,p}\). We generalize well-known counterexamples in \(W^{1,p}\) both for general mappings and for homeomorphisms.
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Acknowledgements
I would like to thank Jan Malý who gave me some useful ideas about the problem. And I thank the my supervisor, Stanislav Hencl, for valuable comments. I also thank Thomas Zürcher for help with the final form of the text.
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The author was supported by the ERC CZ Grant LL1203 of the Czech Ministry of Education.
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Roskovec, T. Higher order Sobolev homeomorphisms and mappings and the Lusin \({\varvec{(N)}}\) condition. Rev Mat Complut 31, 379–406 (2018). https://doi.org/10.1007/s13163-017-0247-0
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DOI: https://doi.org/10.1007/s13163-017-0247-0