  We study a free boundary problem which is motivated by a particular case of
the flow of a non-Newtonian fluid, with a pressure depending yield stress given
by a Drucker-Prager plasticity criterion. We focus on the steady case and
reformulate the equation as a variational problem. The resulting energy has a
term with linear growth while we study the problem in an unbounded domain. We
derive an Euler-Lagrange equation and prove a comparison principle. We are then
able to construct a subsolution and a supersolution which quantify the natural
and expected properties of the solution; in particular they show that the
solution has in fact compact support, the boundary of which is the free
boundary.
  The model describes the flow of a non-Newtonian material on an inclined plane
with walls, driven by gravity. We show that there is a critical angle for a
non-zero solution to exist. Finally, using the sub/supersolutions we give
estimates of the free boundary.
