Geodesic
Oscillations and Concentrations in Sequences of Gradients up to the Boundary
Journal of convex analysis, Tome 20 (2013) no. 3, pp. 723-752

Voir la notice de l'article provenant de la source Heldermann Verlag

\renewcommand{\O}{\Omega} \newcommand{\R}{{\mathbb R}} Oscillations and concentrations in sequences of gradients $\{\nabla u_k\}$, bounded in $L^p(\O; \R^{M\times N})$ if $p>1$ and $\O\subset\R^n$ is a bounded domain with the extension property in $W^{1,p}$, and their interaction with local integral functionals can be described by a generalization of Young measures due to DiPerna and Majda. We characterize such DiPerna-Majda measures, thereby extending a result by A. Ka{\l}amajska and M. Kru\v{z}{\'\i}k [``Oscillations and concentrations in sequences of gradients'', ESAIM, Control Optim. Calc. Var. 14(1) (2008) 71--104], where the full characterization was possible only for sequences subject to a fixed Dirichlet boundary condition. As an application we state a relaxation result for noncoercive multiple-integral functionals.
Classification : 49J45, 35B05
Mots-clés : Sequences of gradients, concentrations, oscillations, quasiconvexity 
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     author = {S. Kr\"omer and M. Kruz{\'\i}k},
     title = {Oscillations and {Concentrations} in {Sequences} of {Gradients} up to the {Boundary}},
     journal = {Journal of convex analysis},
     pages = {723--752},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_3_JCA_2013_20_3_a6/}
}
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S. Krömer; M. Kruzík. Oscillations and Concentrations in Sequences of Gradients up to the Boundary. Journal of convex analysis, Tome 20 (2013) no. 3, pp. 723-752. http://geodesic.mathdoc.fr/item/JCA_2013_20_3_JCA_2013_20_3_a6/