Existence of classical solutions to a free boundary problem for the p-Laplace operator: (I) the exterior convex case

In this paper we prove, under convexity assumptions for the data, the exist ence of classical solutions for a Bernoulli-type free boundary problem, wit h the p-Laplacian as the governing operator. The method employed here origi nates from a pioneering work of A. Beurling where he proves the existence f or the harmonic case in the plane, though with no geometrical restrictions.