About: Young measures supported on invertible matrices

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Description	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 $/det Y_k > 0$. 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 $/det Y_k > 0$. (en)
Title	Young measures supported on invertible matrices Young measures supported on invertible matrices (en)
skos:prefLabel	Young measures supported on invertible matrices Young measures supported on invertible matrices (en)
skos:notation	RIV/67985556:_____/14:00392414!RIV14-GA0-67985556
http://linked.open...avai/predkladatel	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP201/10/0357), P(GAP201/12/0671)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Kružík, Martin
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	56509
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/14:00392414
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Young measures; orientation-preserving mappings; relaxation (en)
http://linked.open.../riv/klicoveSlovo	relaxation Young measures orientation-preserving mappings
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[9C677BE8EC69]
http://linked.open...i/riv/nazevZdroje	Applicable Analysis
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Modern mathematical and computational models for inelastic processes in solids Variational and numerical analysis in nonsmooth continuum mechanics
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	93
http://linked.open...iv/tvurceVysledku	Benešová, Barbora Kružík, Martin Pathó, G.
http://linked.open...ain/vavai/riv/wos	000330718000007
issn	0003-6811
number of pages	19 (xsd:int)
http://bibframe.org/vocab/doi	10.1080/00036811.2012.760039

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