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Jacobian of weak limits of Sobolev homeomorphisms

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Hencl, S., & Onninen, J. (2018). Jacobian of weak limits of Sobolev homeomorphisms. Advances in Calculus of Variations, 11 (1), 65-73. doi:10.1515/acv-2016-0005
Published in
Advances in Calculus of Variations
Authors
Hencl, Stanislav |
Onninen, Jani
Date
2018
Discipline
Matematiikka
Copyright
© Walter de Gruyter GmbH, 2018. Published in this repository with the kind permission of the publisher.

 
Let Ω be a domain in Rn, where n=2,3. Suppose that a sequence of Sobolev homeomorphisms fk:Ω→Rn with positive Jacobian determinants, J(x,fk)>0, converges weakly in W1,p(Ω,Rn), for some p⩾1, to a mapping f. We show that J(x,f)⩾0 a.e. in Ω. Generalizations to higher dimensions are also given.
Publisher
Walter de Gruyter GmbH
ISSN Search the Publication Forum
1864-8258
Keywords
konvergenssi geometria kimmoisuus matematiikka Sobolev homeomorphism weak limits Jacobian convergence geometry elasticity (physical properties) mathematics
DOI
https://doi.org/10.1515/acv-2016-0005
URI

http://urn.fi/URN:NBN:fi:jyu-201804192124

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