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 partial derivative(t)u = Delta phi(u) in a bounded domain with phi smooth, strictly increasing, and sublinear at infinity. Specific assumptions on the behavior of the second derivative of phi 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 infinity) regularity for positive times. Constructive methods, comparison techniques and estimates of Aronson-B & eacute;nilan type are used.