Lecture notes on the DiPerna-Lions theory in abstract measure spaces
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.
The paper is available on the
cvgmt preprint server.