Almost everywhere well-posedness of continuity equations with measure initial data

Luigi Ambrosio; Alessio Figalli

doi:10.1016/j.crma.2010.01.018

Mathematical Analysis/Probability Theory

Almost everywhere well-posedness of continuity equations with measure initial data
[Existence « presque partout » des équations de continuité avec données initiales mesures]

Présenté par : Pierre-Louis Lions

Luigi Ambrosio ¹ ; Alessio Figalli ²

¹ Scuoli Normale Superiore, piazza Cavalieri 7, 56126 Pisa, Italy
² Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712-1082, USA

Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 249-252.

Résumé
Abstract

Dans cette Note, nous présentons des nouveaux résultats concernant l'existence, l'unicité (au sens « presque partout ») et la stabilité pour des équations de continuité avec données initiales mesures. Les preuves de tous ces résultats sont données dans Ambrosio et al. [4], avec aussi des applications à la limite semiclassique pour l'équation de Schrödinger.

The aim of this Note is to present some new results concerning “almost everywhere” well-posedness and stability of continuity equations with measure initial data. The proofs of all such results can be found in Ambrosio et al. [4], together with some application to the semiclassical limit of the Schrödinger equation.

Reçu le : 2009-10-14
Accepté le : 2010-01-13
Publié le : 2010-02-21

DOI : 10.1016/j.crma.2010.01.018

Affiliations des auteurs :

Luigi Ambrosio ¹ ; Alessio Figalli ²

¹ Scuoli Normale Superiore, piazza Cavalieri 7, 56126 Pisa, Italy
² Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712-1082, USA

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Luigi Ambrosio; Alessio Figalli. Almost everywhere well-posedness of continuity equations with measure initial data. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 249-252. doi : 10.1016/j.crma.2010.01.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.01.018/

Bibliographie
Cité par

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Victor Chabu Semiclassical analysis of the Schrödinger equation with conical singularities, Asymptotic Analysis, Volume 103 (2017) no. 4, p. 165 | DOI:10.3233/asy-171423
Luigi Ambrosio Well posedness of ODE’s and continuity equations with nonsmooth vector fields, and applications, Revista Matemática Complutense, Volume 30 (2017) no. 3, p. 427 | DOI:10.1007/s13163-017-0244-3
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Luigi Ambrosio; Alessio Figalli; Gero Friesecke; Johannes Giannoulis; Thierry Paul Corrigendum: Semiclassical Limit of Quantum Dynamics with Rough Potentials and Well‐Posedness of Transport Equations with Measure Initial Data, Communications on Pure and Applied Mathematics, Volume 66 (2013) no. 4, p. 646 | DOI:10.1002/cpa.21440
Luigi Ambrosio; Alessio Figalli; Gero Friesecke; Johannes Giannoulis; Thierry Paul Semiclassical limit of quantum dynamics with rough potentials and well‐posedness of transport equations with measure initial data, Communications on Pure and Applied Mathematics, Volume 64 (2011) no. 9, p. 1199 | DOI:10.1002/cpa.20371
Luigi Ambrosio The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems, Nonlinear Conservation Laws and Applications, Volume 153 (2011), p. 181 | DOI:10.1007/978-1-4419-9554-4_7

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