Noncoercive diffusion equations with Radon measures as initial data
Maria Michaela Porzio, Flavia Smarrazzo, Alberto Tesei · Journal of the London Mathematical Society · 2022
We study Radon measure-valued solutions of the Cauchy–Dirichlet problem for ∂ t u = Δ ϕ ( 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.