Noncoercive diffusion equations with Radon measures as initial data

We study Radon measure-valued solutions of the Cauchy-Dirichlet problem for partial differential tu=Delta phi(u)$\partial _t u = \Delta \phi (u)$ for a continuous, nondecreasing, at most powerlike phi$\phi$. We prove well-posedness and regularity results, which depend on whether or not the initial data charge sets of suitable capacity (determined both by the Laplacian and by the growth order of phi$\phi$), and on suitable compatibility conditions.