Generalized \mathbfW^1,1-Young measures and relaxation of problems with linear growth

2016/11/13 by Margarida Baı́a, Baia, Margarida, Stefan Krömer +3
Mathematics · #26B30 #49J45 #52A99 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1611.04160

openalex publication_date 2016/11/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We completely characterize generalized Young measures generated by sequences of gradients of maps from W^1,1(Ω;\R^M) where Ω⊂\R^N. This extends and completes previous analysis by Kristensen and Rindler where concentrations of the sequence of gradients at the boundary of Ω were excluded. We apply our results to relaxation of non-quasiconvex variational problems with linear growth at infinity. We also link our characterization to Souček spaces \citesoucek, an extension of W^1,1(Ω;\R^M) where gradients are considered as measures on Ω.

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