This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.

Claude Le Bris, École des Ponts ParisTech & Inria, France; Pierre-Louis Lions, Coll. de France & CEREMADE, Uni. Paris-Dauphine, France.