Regularization and Persistence in Nonlinear Diffusion Equations with Measure Initial Data

We study nonnegative Radon measure-valued solutions of the Cauchy-Dirichlet problem for ∂ t u = Δϕ(u) in a bounded domain with ϕ smooth, strictly increasing, and sublinear at infinity. Specific assumptions on the behaviour of the second derivative of ϕ for large arguments are also made. Conditions are given under which parts of the initial measure persist, or solutions gain L 1 (or even L ∞ ) regularity for positive times. Constructive methods, comparison techniques and estimates of Aronson-Béenilan type are used.