Very weak solutions of singular porous medium equations with measure data
Verena Bögelein, Frank Duzaar, Ugo Gianazza · Communications on Pure & Applied Analysis · 2015
We consider non-homogeneous, singular ($ 0 < m < 1 $) porous medium type equations with a non-negative Radon-measure $\mu$ having finite total mass $\mu(E_T)$ on theright-hand side. We deal with a Cauchy-Dirichlet problem for these type of equations, with homogeneous boundary conditions on the parabolic boundary of the domain $E_T$, and we establish the existence of a solution in the sense of distributions.Finally, we show thatthe constructed solution satisfies linear pointwise estimates via linearRiesz potentials.