Characterization of gradient young measures generated by homeomorphisms in the plane

0456299 - ÚTIA 2017 RIV GB eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR GA14-15264S; GA ČR GAP201/10/0357; GA ČR(CZ) GAP201/12/0671
Grant ostatní: GA ČR(CZ) GA14-00420S; GA ČR(CZ) GAP107/12/0121
Institucionální podpora: RVO:67985556
Klíčová slova: homeomorphism * orientation preservation
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.540, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0258403