Title: Young measure, superposition and transport

Authors: Patrick Bernard

Issue: Volume 57 (2008), Issue 1, 247-276

Abstract: We discuss a space of Young measures in connection with some variational problems. We use it to present a proof of the Theorem of Tonelli on the existence of minimizing curves. We generalize a recent result of Ambrosio, Gigli and Savar\'e on the decomposition of the weak solutions of the transport equation. We also prove, in the context of Mather theory, the equality between Closed measures and Holonomic measures.