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Lecture notes on the DiPerna–Lions theory in abstract measure spaces
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 26 (2017) no. 4, pp. 729-766.

These notes collect the lectures given by the first author in Toulouse, April 2014, on the well-posedness theory for continuity and transport equation in metric measure spaces, summarizing the joint work appeared in Analysis and PDE. The last part of the notes covers also more recent developments, due to the second author, on diffusion operators on metric measure spaces.

Ces notes résument les leçons données à Toulouse en avril 2014 par le premier auteur sur le caractère bien ou mal posé des problèmes liés aux équations de continuité et de transport dans les espaces métriques mesurés, reprenant un travail commun publié dans Analysis and PDE. La dernière partie des notes couvre également des développements plus récents, dus au second auteur, sur les opérateurs de diffusion dans les espaces métriques mesurés.

Published online:
DOI: 10.5802/afst.1551
Luigi Ambrosio 1; Dario Trevisan 2

1 Scuola Normale Superiore, Pisa, Italy
2 Università di Pisa, Italy
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Lecture notes on the {DiPerna{\textendash}Lions} theory in abstract measure spaces},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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Luigi Ambrosio; Dario Trevisan. Lecture notes on the DiPerna–Lions theory in abstract measure spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 26 (2017) no. 4, pp. 729-766. doi : 10.5802/afst.1551. https://afst.centre-mersenne.org/articles/10.5802/afst.1551/

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