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

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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∇u] ϱ, 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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     title = {Quasiconvexity at the boundary and concentration effects generated by gradients},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {679--700},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {3},
     year = {2013},
     doi = {10.1051/cocv/2012028},
     mrnumber = {3092357},
     zbl = {1277.49014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012028/}
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Kružík, Martin. Quasiconvexity at the boundary and concentration effects generated by gradients. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 679-700. doi: 10.1051/cocv/2012028

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