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- Title
SOME REMARKS ON SOBOLEV AND BI-SOBOLEV MAPPINGS.
- Authors
D'Onofrio, Luigi; Molica Bisci, Giovanni
- Abstract
In this note, we present the state-of-the-art theory of bi-Sobolev mappings. We recall that f is a Sobolev homeomorphism if f belongs to W loc 1 , 1 ∩ Hom (Ω ; Ω ′) , and f is a bi-Sobolev map if and only if f and f - 1 are 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).
- Subjects
GEOMETRIC function theory
- Publication
Journal of Mathematical Sciences, 2024, Vol 280, Issue 1, p50
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-023-06665-x