Geodesic
Regularity of a~Solution to the~Multidimensional Free Boundary Problem for the~Porous Medium Equation
Matematičeskie trudy, Tome 5 (2002) no. 2, pp. 38-91.

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The regularity properties of solutions to the initial boundary value problem with free boundary for the nonlinear degenerate equation $u_t=\Delta(u^m)$, $m>1$, are studied in the multi-dimensional case. The condition $u=0$ holds on the free boundary whose velocity obeys the Darcy law. The differential properties of the free boundary are established in dependence on the smoothness of the initial data. 
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B. V. Bazalii; N. V. Krasnoshchek. Regularity of a~Solution to the~Multidimensional Free Boundary Problem for the~Porous Medium Equation. Matematičeskie trudy, Tome 5 (2002) no. 2, pp. 38-91. http://geodesic.mathdoc.fr/item/MT_2002_5_2_a1/

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