Revista Matemática Iberoamericana

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Volume 2, Issue 4, 1986, pp. 357–366
DOI: 10.4171/RMI/38

Published online: 1986-12-31

Optimal Regularity for One-Dimensional Porous Medium Flow

D. G. Aronson[1] and Luis A. Caffarelli[2]

(1) University of Minnesota, Minneapolis, USA
(2) University of Texas at Austin, USA

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

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Aronson D., Caffarelli Luis: Optimal Regularity for One-Dimensional Porous Medium Flow. Rev. Mat. Iberoam. 2 (1986), 357-366. doi: 10.4171/RMI/38