Young measures, superposition and transport

By P. Bernard. 2007

80 citations recorded by the source corpus.

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 Savare 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.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ad824668c3f4805260457334550a59d79036b22a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Hélène Frankowska
2. Giuseppe Savar'e
3. S. Lisini
4. Benoît Bonnet
5. Giulia Cavagnari
6. Carlo Orrieri
7. Nicola Gigli
8. Luigi Ambrosio

In Statistical and Nonlinear Physics

1. S. Lisini
2. Hélène Frankowska
3. Giuseppe Savar'e
4. Giulia Cavagnari
5. Carlo Orrieri
6. Benoît Bonnet

In Statistics and Probability

1. S. Lisini
2. Hélène Frankowska
3. Giuseppe Savar'e
4. Giulia Cavagnari
5. Carlo Orrieri
6. Benoît Bonnet

Citations in the corpus

• Differential inclusions in Wasserstein spaces: The Cauchy-Lipschitz framework (2020, background): “the seminal contribution [18]) was proposed in [53] for continuity equations.”
• Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: Equivalence and Gamma-convergence (2020, methodology): “Let us now recall the definition of Young measure (see [7, 20]) and a density result which will turn out to be a crucial tool in our treatment.”