Oscillation and concentration effects described by Young measures which control discontinuous functions

Abstract

We study oscillation and concentration effects for sequences of compositions $\{ f(u^\nu)\}_{\nu\in\mathbb N}$ of $\mu$-measurable functions $u^\nu\colon \Omega\rightarrow{\mathbb R}^{m}$ where $\Omega$ is the compact subset of ${\mathbb R}^n$ and $f$ is the (possibly) discontinuous function. The limits are described in terms of Young measures which can control discontinuous functions recently introduced in [A. Kalamajska, On Young measures controlling discontinuous functions , J. Conv. Anal. 13 (2006), no. 1, 177–192].