A filtration problem through a heterogeneous porous medium (Q1430453)

The authors study a two-dimensional free boundary problem modeling a steady state flow which is governed by a nonlinear Darcy law through a heterogeneous porous medium. Under a rather general condition on the permeability and for \(C^1\)-domains they prove that the free boundary can be represented locally as the graph of a continuous function. This result is then exploited to prove uniqueness of an \(S_3\)-connected solution under some additional structural assumptions on the domain and the filtration law.