Lecture Notes on the Diperna-lions Theory in Abstract Measure Spaces
نویسنده
چکیده
Contents 1. Introduction 1 2. Reminders on the Cauchy-Lipschitz theory 4 3. Nonsmooth vector fields in Euclidean spaces 4 4. Abstract setup 7 5. Derivations and their regularity 10 6. Eulerian side 11 6.1. Existence of solutions to the continuity equation 11 6.2. Uniqueness of solutions to the continuity equation 14 7. Lagrangian side 16 7.1. ODE's associated to derivations and Regular Lagrangian Flows 16 7.2.
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