Very weak solutions of singular porous medium equations with measure data

Verena Bögelein; Frank Duzaar; Ugo Gianazza

doi:10.3934/cpaa.2015.14.23

Article Contents

2015, Volume 14, Issue 1: 23-49. Doi: 10.3934/cpaa.2015.14.23

This issue Previous Article On the Dirichlet boundary value problem for the normalized $p$-laplacian evolution Next Article On the validity of the Euler-Lagrange system

Very weak solutions of singular porous medium equations with measure data

1.
Department Mathematik, Universität Erlangen--Nürnberg, Cauerstr. 11, 91056 Erlangen
2.
Dipartimento di Matematica "F. Casorati”, Università di Pavia, Via Ferrata 1, 27100 Pavia

Received: April 2014

Revised: April 2014

Published: January 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K67; Secondary: 31B15.

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