Institute of Information Theory and Automation

You are here

Bibliography

Journal Article

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

Krömer Stefan

: Archive for Rational Mechanics and Analysis vol.238, 3 (2020), p. 1113-1155

: GF19-29646L, GA ČR, 8J19AT013, GA MŠk

: topological degree, Nonlinear Elasticity, global invertibility, approximate invertibility on the boundary, orientation-preserving deformations

: 10.1007/s00205-020-01559-7

: http://library.utia.cas.cz/separaty/2020/MTR/kromer-0531615.pdf

: https://link.springer.com/article/10.1007/s00205-020-01559-7

(eng): 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.

: BA

: 10102

2019-01-07 08:39