Young measures, superposition and transport

Details Young measures, superposition and transport Young measures, superposition and transport

2007-01-16

arxiv.org/abs/math/0701451v2

Indiana University Mathematics Journal 57, 1 (2008) 247-276

Mathematics

Dynamical Systems

Scientific paper

10.1512/iumj.2008.57.3163

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.

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