Strong solutions to the Richards equation in the unsaturated zone

We study the unsaturated case of the Richards equation in three space dimensions with Dirichlet boundary data. We first establish an a priori L ∞ -estimate. With its help, by means of a fixed point argument we prove global in time existence of a unique weak solution in Sobolev spaces. Finally, we are able to improve the regularity of this weak solution in order to gain a strong one.