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

摘要

In this paper we prove, under convexity assumptions for the data, the existence of classical solutions for a Bernoulli-type free boundary problem, with the p-Laplacian as the governing operator. The method employed here originates from a pioneering work of A. Beurling where he proves the existence for the harmonic case in the plane, though with no geometrical restrictions. [References: 21]