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Very weak solutions of singular porous medium equations with measure data

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  • 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 the right-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 that the constructed solution satisfies linear pointwise estimates via linear Riesz potentials.
    Mathematics Subject Classification: Primary: 35K67; Secondary: 31B15.

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