A non-homogeneous elliptic problem dealing with the level set formulation of the inverse mean curvature flow

In the present paper we study the Dirichlet problem for the equation−div(Du|Du|)+|Du|=f in an unbounded domain Ω⊂RNΩ⊂RN, where the datum f is bounded and nonnegative. We point out that the only hypothesis assumed on ∂Ω is that of being Lipschitz-continuous. This problem is the non-homogeneous extension of the level set formulation of the inverse mean curvature flow in a Euclidean space. We introduce a suitable concept of weak solution, for which we prove existence, uniqueness and a comparison principle.