Quasiconvexity at the boundary and concentration effects generated by gradients

TL;DR

This paper characterizes DiPerna-Majda measures generated by gradient sequences, focusing on their behavior at domain boundaries using sphere compactification, which advances understanding of gradient concentration effects.

Contribution

It provides a precise description of boundary behavior of DiPerna-Majda measures in the context of gradient sequences and boundary compactification.

Findings

Characterization of DiPerna-Majda measures at the boundary

Description of measure behavior using sphere compactification

Insights into gradient concentration effects at domain boundaries

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 $\R^{m\times n}$ by the sphere.