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SOME REMARKS ON SOBOLEV AND BI-SOBOLEV MAPPINGS.
- Source :
-
Journal of Mathematical Sciences . Mar2024, Vol. 280 Issue 1, p50-60. 11p. - Publication Year :
- 2024
-
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). [ABSTRACT FROM AUTHOR]
- Subjects :
- *GEOMETRIC function theory
Subjects
Details
- Language :
- English
- ISSN :
- 10723374
- Volume :
- 280
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 175695654
- Full Text :
- https://doi.org/10.1007/s10958-023-06665-x