JournalsrmiVol. 2, No. 4pp. 357–366

Optimal Regularity for One-Dimensional Porous Medium Flow

  • D. G. Aronson

    University of Minnesota, Minneapolis, USA

  • Luis A. Caffarelli

    University of Texas at Austin, USA
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Abstract

We give a new proof of the Lipschitz continuity with respect to of the pressure in a one dimensional porous medium flow. As is shown by the Barenblatt solution, this is the optimal -regularity for the pressure. Our proof is based on the existence and properties of a certain selfsimilar solution.

Cite this article

D. G. Aronson, Luis A. Caffarelli, Optimal Regularity for One-Dimensional Porous Medium Flow. Rev. Mat. Iberoam. 2 (1986), no. 4, pp. 357–366

DOI 10.4171/RMI/38