Global invertibility for orientation-preserving Sobolev maps via invertibility on or near the boundary

0531615 - ÚTIA 2021 RIV DE eng J - Journal Article
Krömer, Stefan
Global invertibility for orientation-preserving Sobolev maps via invertibility on or near the boundary.
Archive for Rational Mechanics and Analysis. Roč. 238, č. 3 (2020), s. 1113-1155. ISSN 0003-9527. E-ISSN 1432-0673
R&D Projects: GA ČR(CZ) GF19-29646L; GA MŠMT(CZ) 8J19AT013
Institutional support: RVO:67985556
Keywords : topological degree * Nonlinear Elasticity * global invertibility * approximate invertibility on the boundary * orientation-preserving deformations
OECD category: Applied mathematics
Impact factor: 2.793, year: 2020
Method of publishing: Open access
http://library.utia.cas.cz/separaty/2020/MTR/kromer-0531615.pdf https://link.springer.com/article/10.1007/s00205-020-01559-7

By a result of Ball (Proc R Soc Edinb Sect A Math 88:315–328, 1981. https://doi.org/10.1017/S030821050002014X), a locally orientation preserving Sobolev map is almost everywhere globally invertible whenever its boundary values admit a homeomorphic extension. As shown here for any dimension, the conclusions of Ball’s theorem and related results can be reached while completely avoiding the problem of homeomorphic extension. For suitable domains, it is enough to know that the trace is invertible on the boundary or can be uniformly approximated by such maps. An application in Nonlinear Elasticity is the existence of homeomorphic minimizers with finite distortion whose boundary values are not fixed. As a tool in the proofs, strictly orientation-preserving maps and their global invertibility properties are studied from a purely topological point of view.
Permanent Link: http://hdl.handle.net/11104/0310649