Noncoercive diffusion equations with Radon measures as initial data

We study Radon measure‐valued solutions of the Cauchy–Dirichlet problem for ∂tu=Δϕ(u)$\partial _t u = \Delta \phi (u)$ for a continuous, nondecreasing, at most powerlike ϕ$\phi$. 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 ϕ$\phi$), and on suitable compatibility conditions.