Revista Matemática Complutense

, Volume 31, Issue 2, pp 379–406 | Cite as

Higher order Sobolev homeomorphisms and mappings and the Lusin \({\varvec{(N)}}\) condition

  • Tomáš Roskovec


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.


Lusin condition Sobolev space Area formula 

Mathematics Subject Classification




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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© Universidad Complutense de Madrid 2017

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Informatics, Faculty of EconomicsUniversity of South Bohemia in České BudějoviceČeské BudějoviceCzech Republic

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