Electron. J. Diff. Equ., Vol. 2015 (2015), No. 101, pp. 1-25.

Pointwise estimates for porous medium type equations with low order terms and measure data

Stefan Sturm

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 Bögelein, Duzaar and Gianazza [3, Theorem 1.2], since the problem and the structure conditions considered here, are more univ ersal.

Submitted January 13, 2015. Published April 15, 2015.
Math Subject Classifications: 35K65, 35K20, 31B15.
Key Words: Porous medium equation; measure data; Riesz potential estimates; degenerate parabolic equations.

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Stefan Sturm
Fachbereich Mathematik
Paris-Lodron-Universität Salzburg
5020 Salzburg, Austria
email: Stefan.Sturm@sbg.ac.at

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