Abstract
AbstractIn this note, we present the state-of-the-art theory of bi-Sobolev mappings. We recall thatfis aSobolev homeomorphismiffbelongs to$$W^{1,1}_\text {loc}\cap \textrm{Hom}(\Omega ; \Omega ')$$Wloc1,1∩Hom(Ω;Ω′), andfis abi-Sobolev mapif and only iffand$$f^{-1}$$f-1are Sobolev homeomorphisms. This concept, introduced in Hencl et al. (J. Math. Anal. Appl. 355, 22–32 2009), plays a central role in Geometric Function Theory. For instance, we just mention here that maps of bi-Sobolev type are strictly related to the notion of mappings of finite distortion; see, among others, the papers (Hencl and Koskela 2014) Pratelli (Nonlinear Anal. 154, 258–268 2017).
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilitáá e le loro Applicazioni
Università Parthenope di Napoli
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics,Statistics and Probability
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