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Journal Article

Young measures supported on invertible matrices

Benešová Barbora, Kružík Martin, Pathó G.

: Applicable Analysis vol.93, 1 (2014), p. 105-123

: GAP201/12/0671, GA ČR, GAP201/10/0357, GA ČR

: Young measures, orientation-preserving mappings, relaxation

: 10.1080/00036811.2012.760039

: http://library.utia.cas.cz/separaty/2013/MTR/kruzik-young measures supported on invertible matrices.pdf

(eng): 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 $/det Y_k > 0$.

: BA

2019-01-07 08:39