Porous Medium Type Equations with Measure Data and Potential Estimates
Verena Bögelein, Frank Duzaar, Ugo Gianazza · SIAM Journal on Mathematical Analysis · 2013
We consider nonhomogeneous, degenerate ($m>1$) porous medium type equations with a nonnegative Radon measure $\mu$ having finite total mass $\mu(E_T)$ on the right-hand side, and we derive linear pointwise estimates for solutions via Riesz potentials. Then, we deal with a Cauchy--Dirichlet problem for the same equation, 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.