Global invertibility for orientation-preserving Sobolev maps via invertibility on or near the boundary
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F20%3A00531615" target="_blank" >RIV/67985556:_____/20:00531615 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00205-020-01559-7" target="_blank" >https://link.springer.com/article/10.1007/s00205-020-01559-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00205-020-01559-7" target="_blank" >10.1007/s00205-020-01559-7</a>
Alternative languages
Result language
angličtina
Original language name
Global invertibility for orientation-preserving Sobolev maps via invertibility on or near the boundary
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Archive for Rational Mechanics and Analysis
ISSN
0003-9527
e-ISSN
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Volume of the periodical
238
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
43
Pages from-to
1113-1155
UT code for WoS article
000556617900001
EID of the result in the Scopus database
2-s2.0-85089080409