The smoothing property for a class of doubly nonlinear parabolic equations

We consider a class of doubly nonlinear parabolic equations used in modeling free boundaries with a finite speed of propagation. We prove that nonnegative weak solutions satisfy a smoothing property; this is a well-known feature in some particular cases such as the porous medium equation or the parabolic p p -Laplace equation. The result is obtained via regularization and a comparison theorem.