# Oscillations and concentrations in sequences of gradients

Agnieszka Kałamajska; Martin Kružík

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

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topKałamajska, Agnieszka, and Kružík, Martin. "Oscillations and concentrations in sequences of gradients." ESAIM: Control, Optimisation and Calculus of Variations 14.1 (2010): 71-104. <http://eudml.org/doc/90866>.

@article{Kałamajska2010,

abstract = {
We use DiPerna's and Majda's generalization of Young measures to describe oscillations and concentrations in sequences of gradients, $\\{\nabla u_k\\}$, bounded in $L^p(\Omega;\{\mathbb R\}^\{m\times n\})$
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 Ω are
required and links with lower semicontinuity results by Meyers and
by Acerbi and Fusco are also discussed.
},

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

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

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

language = {eng},

month = {3},

number = {1},

pages = {71-104},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/90866},

volume = {14},

year = {2010},

}

TY - JOUR

AU - Kałamajska, Agnieszka

AU - Kružík, Martin

TI - Oscillations and concentrations in sequences of gradients

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

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, $\{\nabla u_k\}$, bounded in $L^p(\Omega;{\mathbb R}^{m\times n})$
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 Ω 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; sequences of gradients

UR - http://eudml.org/doc/90866

ER -

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