Oscillations and concentrations in sequences of gradients
ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 1, pp. 71-104.

We use DiPerna’s and Majda’s generalization of Young measures to describe oscillations and concentrations in sequences of gradients, {u k }, bounded in L p (Ø; m×n ) if p>1 and Ω 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.

DOI: 10.1051/cocv:2007051
Classification: 49J45, 35B05
Keywords: sequences of gradients, concentrations, oscillations, quasiconvexity
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Kałamajska, Agnieszka; Kružík, Martin. Oscillations and concentrations in sequences of gradients. ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 1, pp. 71-104. doi : 10.1051/cocv:2007051. http://www.numdam.org/articles/10.1051/cocv:2007051/

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