# Quasiconvexity at the boundary and concentration effects generated by gradients

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

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

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topKružík, 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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