Quasiconvexity at the boundary and concentration effects generated by gradients

Martin Kružík

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 3, page 679-700
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Kružík, Martin. "Quasiconvexity at the boundary and concentration effects generated by gradients." ESAIM: Control, Optimisation and Calculus of Variations 19.3 (2013): 679-700. <http://eudml.org/doc/272785>.

@article{Kružík2013,
abstract = {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.},
author = {Kružík, Martin},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {bounded sequences of gradients; concentrations; oscillations; quasiconvexity at the boundary; weak lower semicontinuity},
language = {eng},
number = {3},
pages = {679-700},
publisher = {EDP-Sciences},
title = {Quasiconvexity at the boundary and concentration effects generated by gradients},
url = {http://eudml.org/doc/272785},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Kružík, Martin
TI - Quasiconvexity at the boundary and concentration effects generated by gradients
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 3
SP - 679
EP - 700
AB - 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.
LA - eng
KW - bounded sequences of gradients; concentrations; oscillations; quasiconvexity at the boundary; weak lower semicontinuity
UR - http://eudml.org/doc/272785
ER -

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