Young measures, superposition and transport

Bernard, Patrick

Bernard, Patrick (2008), Young measures, superposition and transport, Indiana University Mathematics Journal, 57, 1, p. 247-276. http://dx.doi.org/10.1512/iumj.2008.57.3163

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00124907/en/

Date

2008

Journal name

Indiana University Mathematics Journal

Volume

Number

Publisher

Bloomington, Ind.

Pages

247-276

Abstract (EN)

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 Savaré 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.

Subjects / Keywords

Equations différentielles