Lecture notes on the DiPerna–Lions theory in abstract measure spaces

Ambrosio, Luigi; Trevisan, Dario

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 26 (2017) no. 4, pp. 729-766.

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.

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.

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