Pointwise estimates for porous medium type equations with low order terms and measure data
Stefan Sturm · DOAJ (DOAJ: Directory of Open Access Journals) · 2015
We study a Cauchy-Dirichlet problem with homogeneous boundary conditions on the parabolic boundary of a space-time cylinder for degenerate porous medium type equations with low order terms and a non-negative, finite Radon measure on the right-hand side. The central objective is to acquire linear pointwise estimates for weak solutions in terms of Riesz potentials. Our main result, Theorem 1.1, generalizes an estimate previously obtained by Bogelein, Duzaar and Gianazza [3, Theorem 1.2], since the problem and the structure conditions considered here, are more univ ersal.