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