This lecture deals with the following problem, let us call it (P): \begin{equation} \left\{ \begin{array}{ll} \displaystyle - {\rm div} \left(\frac{Du}{\vert Du \vert} \right) + \vert Du \vert = f\,, \quad & \hbox{in} \ \ \Omega\,; \\ \\ u = 0\,, \quad & \hbox{on} \ \ \partial E_0\,; \\ \\ \displaystyle\lim_{\vert x \vert \to \infty} u(x) = +\infty\,; \end{array} \right. \end{equation} where \Omega = {\mathbb R}^N \backslash \overline{E_0}, being E_0 an open bounded set having Lipschitz-continuous boundary, and 0 \leq f \in L^{\infty}(\Omega). We introduce a natural concept of weak solution and prove existence, uniqueness and a comparison principle. In the homogeneous case, f=0, problem (P) deals with the level set formulation of the inverse mean curvature flow in an Euclidean space, studied by Huisken-Ilmanen and Moser. To prove the existence of solution of problem (P) we approximate it by the following problems related to the p-Laplacian operator: \begin{equation} \left\{ \begin{array}{ll} - \Delta_p(u) + \vert \nabla u \vert^p = f\,, \quad & \hbox{in} \ \ \Omega\,; \\ \\ u = 0\,, \quad & \hbox{on} \ \ \partial E_0\,; \\ \\ \displaystyle\lim_{\vert x \vert \to \infty} u(x) = +\infty\,; \end{array} \right. \end{equation} where \Delta_p(u):= {\rm div} \left( \vert \nabla u \vert^{p-2} \nabla u \right), with 1 < p \le2. We show that the approximating problems are well-posed. Let us point out that this result is new, as far as we know, and interesting in itself.