Characterization of gradient young measures generated by homeomorphisms in the plane

0456299 - ÚTIA 2017 RIV GB eng J - Journal Article
Benešová, B. - Kružík, Martin
Characterization of gradient young measures generated by homeomorphisms in the plane.
ESAIM-Control Optimisation and Calculus of Variations. Roč. 22, č. 1 (2016), s. 267-288. ISSN 1292-8119. E-ISSN 1262-3377
R&D Projects: GA ČR GA14-15264S; GA ČR GAP201/10/0357; GA ČR(CZ) GAP201/12/0671
Grant - others:GA ČR(CZ) GA14-00420S; GA ČR(CZ) GAP107/12/0121
Institutional support: RVO:67985556
Keywords : homeomorphism * orientation preservation
Subject RIV: BA - General Mathematics
Impact factor: 1.540, year: 2016
http://library.utia.cas.cz/separaty/2016/MTR/kruzik-0456299.pdf

We characterize Young measures generated by gradients of bi-Lipschitz orientation-preserving maps in the plane. This question is motivated by variational problems in nonlinear elasticity where the orientation preservation and injectivity of the admissible deformations are key requirements. These results enable us to derive new weak lower semicontinuity results for integral functionals depending on gradients. As an application, we show the existence of a minimizer for an integral functional with nonpolyconvex energy density among bi-Lipschitz homeomorphisms.
Permanent Link: http://hdl.handle.net/11104/0258403