Regularization and persistence in nonlinear diffusion equations with measure initial data

In this paper, we study nonnegative Radon measure-valued solutions of the Cauchy–Dirichlet problem for [Formula: see text] in a bounded domain with [Formula: see text] smooth, strictly increasing, and sublinear at infinity. Specific assumptions on the behavior of the second derivative of [Formula: see text] for large arguments are also made. Conditions are given under which parts of the initial measure persist, or solutions gain [Formula: see text] (or even [Formula: see text]) regularity for positive times. Constructive methods, comparison techniques and estimates of Aronson–Bénilan type are used.