Oscillations and concentrations up to the boundary

2011/09/14 by Krömer, Stefan, Kružík, Martin
#35B05 #49J45 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.3020

Abstract

Oscillations and concentrations in sequences of gradients \∇ u_k\, bounded in L^p(Ω;\R^{M× N}) if p>1 and Ω⊂\Rⁿ 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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