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This work presents a new proof of the recent characterization theorem forgeneralized Young measures generated by sequences in BV by Kristensen and theauthor [Arch. Ration. Mech. Anal. 197 (2010), 539-598]. The present argument isbased on a localization technique together with a local Hahn-Banach argument innovel function spaces combined with an application of Alberti's Rank-OneTheorem. This strategy avoids employing a relaxation theorem as in thepreviously known proof, and the new tools introduced in its course should proveuseful in other contexts as well. In particular, we introduce homogeneous Youngmeasures, separately at regular and singular points, which exhibit ratherdifferent behaviour than the classical homogeneous Young measures. As anapplication, we show how for BV-Young measures with an atomic part one can finda generating sequence respecting this structure.

A local proof for the characterization of Young measures generated by sequences in BV