# Oscillations and concentrations in sequences of gradients

Martin Kružík; Agnieszka Kałamajska

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 14, Issue: 1, page 71-104
- ISSN: 1292-8119

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topKružík, Martin, and Kałamajska, Agnieszka. "Oscillations and concentrations in sequences of gradients." ESAIM: Control, Optimisation and Calculus of Variations 14.1 (2008): 71-104. <http://eudml.org/doc/246024>.

@article{Kružík2008,

abstract = {We use DiPerna’s and Majda’s generalization of Young measures to describe oscillations and concentrations in sequences of gradients, $\lbrace \nabla u_k\rbrace $, bounded in $L^p(Ø;\mathbb \{R\}^\{m\times n\})$ if $p > 1$ and $\Omega \subset \mathbb \{R\}^n$ is a bounded domain with the extension property in $W^\{1,p\}$. Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of $\Omega $ are required and links with lower semicontinuity results by Meyers and by Acerbi and Fusco are also discussed.},

author = {Kružík, Martin, Kałamajska, Agnieszka},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {sequences of gradients; concentrations; oscillations; quasiconvexity},

language = {eng},

number = {1},

pages = {71-104},

publisher = {EDP-Sciences},

title = {Oscillations and concentrations in sequences of gradients},

url = {http://eudml.org/doc/246024},

volume = {14},

year = {2008},

}

TY - JOUR

AU - Kružík, Martin

AU - Kałamajska, Agnieszka

TI - Oscillations and concentrations in sequences of gradients

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2008

PB - EDP-Sciences

VL - 14

IS - 1

SP - 71

EP - 104

AB - We use DiPerna’s and Majda’s generalization of Young measures to describe oscillations and concentrations in sequences of gradients, $\lbrace \nabla u_k\rbrace $, bounded in $L^p(Ø;\mathbb {R}^{m\times n})$ if $p > 1$ and $\Omega \subset \mathbb {R}^n$ is a bounded domain with the extension property in $W^{1,p}$. Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of $\Omega $ are required and links with lower semicontinuity results by Meyers and by Acerbi and Fusco are also discussed.

LA - eng

KW - sequences of gradients; concentrations; oscillations; quasiconvexity

UR - http://eudml.org/doc/246024

ER -

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