Young measures supported on invertible matrices

0392414 - ÚTIA 2014 RIV GB eng J - Článek v odborném periodiku
Benešová, Barbora - Kružík, Martin - Pathó, G.
Young measures supported on invertible matrices.
Applicable Analysis. Roč. 93, č. 1 (2014), s. 105-123. ISSN 0003-6811. E-ISSN 1563-504X
Grant CEP: GA ČR(CZ) GAP201/12/0671; GA ČR GAP201/10/0357
Institucionální podpora: RVO:67985556 ; RVO:61388998
Klíčová slova: Young measures * orientation-preserving mappings * relaxation
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.803, rok: 2014
http://library.utia.cas.cz/separaty/2013/MTR/kruzik-young measures supported on invertible matrices.pdf

Motivated by variational problems in nonlinear elasticity, we explicitly characterize the set of Young measures generated by gradients of a uniformly bounded sequence in $W^{1,/infty}(/O;/R^n)$ where the inverted gradients are also bounded in $L^/infty(/O;/R^{n/times n})$. This extends the original results due to D.~Kinderlehrer and P.~Pedregal /cite{k-p1}. Besides, we completely describe Young measures generated by a sequence of matrix-valued mappings $/{Y_k/}_{k/in/N} /subset L^p(/O;/R^{n/times n})$, such that $/{Y_k^{-1}/}_{k/in/N} /subset L^p(/O;/R^{n/times n})$ is bounded, too, and the generating sequence satisfies the constraint $/det Y_k > 0$.
Trvalý link: http://hdl.handle.net/11104/0221746