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arXiv · 1109.3020

Oscillations and concentrations up to the boundary

Stefan Krömer·Martin Kružík
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Abstract

Oscillations and concentrations in sequences of gradients $\{\nabla u_k\}$, bounded in $L^p(Ω;\R^{M\times N})$ if $p>1$ and $Ω\subset\R^n$ is a bounded domain with the extension property in $W^{1,p}$, and their interaction with local integral functionals can be described by a generalization of Young measures due to DiPerna and Majda. We characterize such DiPerna-Majda measures, thereby extending a result by Kałamajska and Kruž\'ık (2008), where the full characterization was possible only for sequences subject to a fixed Dirichlet boundary condition. As an application we state a relaxation result for noncoercive multiple-integral functionals.

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Stefan Krömer, Martin Kružík. 2011-09-14. Oscillations and concentrations up to the boundary. https://arxiv.org/abs/1109.3020

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