Quasiconvexity at the boundary and concentration effects generated by gradients
ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 3, pp. 679-700.

We characterize generalized Young measures, the so-called DiPerna-Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the compactification of ℝm × n by the sphere. We show that this characterization is closely related to the notion of quasiconvexity at the boundary introduced by Ball and Marsden [J.M. Ball and J. Marsden, Arch. Ration. Mech. Anal. 86 (1984) 251-277]. As a consequence we get new results on weak W1,2(Ω; ℝ3) sequential continuity of u → a· [Cof∇uϱ, where Ω ⊂ ℝ3 has a smooth boundary and a,ϱ are certain smooth mappings.

DOI: 10.1051/cocv/2012028
Classification: 49J45, 35B05
Keywords: bounded sequences of gradients, concentrations, oscillations, quasiconvexity at the boundary, weak lower semicontinuity
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Kružík, Martin. Quasiconvexity at the boundary and concentration effects generated by gradients. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 3, pp. 679-700. doi : 10.1051/cocv/2012028. http://www.numdam.org/articles/10.1051/cocv/2012028/

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