Regularity of a solution to the multi-dimensional free boundary problem for the porous medium equation (Q1876410)

The regularity properties of solutions to the initial-boundary value problem with free boundary for nonlinear degenerate equation \(u_t=\Delta (u^m)\), \(m>1\), are studied in the multi-dimensional case. The condition \(u=0\) holds for the free boundary whose velocity obeys Darcy law. The differential properties of the free boundary are established depending on the smoothness of the initial data. This is an English translation of the authors' article [Mat. Tr. 5, No. 2, 38--91 (2002; Zbl 1013.76093)].