The Dirichlet problem for a singular elliptic equation arising in the level set formulation of the inverse mean curvature flow

In the present paper we consider the Dirichlet problem associated with a nonlinear singular elliptic equation whose differential operator arises in the level set formulation of the inverse mean curvature flow; namely, we study [Image omitted] We introduce a suitable concept of weak solution, for which we prove existence and uniqueness of the homogeneous Dirichlet problem in a bounded open set of R N for data f belonging to suitable Lebesgue spaces. Moreover, examples of explicit solutions are shown.