Calculus of Variations and Geometric Measure Theory

A. Arroyo-Rabasa - J. Diermeier

Generalized multi-scale Young measures

created by arroyorabasa on 25 Jun 2019



Inserted: 25 jun 2019

Year: 2019

ArXiv: 1901.04755 PDF


This paper is devoted to the construction of generalized multi-scale Young measures, which are the extension of Pedregal's multi-scale Young measures Trans. Amer. Math. Soc. 358 (2006), pp. 591-602 to the setting of generalized Young measures introduced by DiPerna and Majda Comm. Math. Phys. 108 (1987), pp. 667-689. As a tool for variational problems, these are well-suited objects for the study (at different length-scales) of oscillation and concentration effects of convergent sequences of measures. Important properties of multi-scale Young measures such as compactness, representation of non-linear compositions, localization principles, and differential constraints are extensively developed in the second part of this paper. As an application, we use this framework to address the $\Gamma$-limit characterization of the homogenized limit of convex integrals defined on spaces of measures satisfying a general linear PDE constraint.