Electronic Journal of Differential Equations,
Vol. 1995(1995), No. 08, pp. 1-20.

Title: A Free Boundary Problem for the $p$-Laplacian: Uniqueness, 
       Convexity, and Successive Approximation of Solutions

Authors: A. Acker (Wichita State Univ., KS, USA)
         R. Meyer (Northwestern Missouri State Univ., Maryville, MO, USA)

Abstract: We prove convergence of a trial free boundary method to a 
classical solution of a Bernoulli-type free boundary
problem for the $p$-Laplace equation, $ 1 < p < \infty $.  
In addition, we prove the existence of a classical solution in $N$
dimensions when $p = 2$ and, for $ 1 < p < \infty $, results on 
uniqueness and starlikeness of the free boundary and continuous
dependence on the fixed boundary and on the free boundary data. 
Finally, as an application of the trial free boundary method, we
prove (also for $ 1 < p < \infty $) that the free boundary is convex 
when the fixed boundary is convex.

Submitted June 12, 1995. Published June 21, 1995.
Math Subject Classification: 35J20, 35A35, 35R35.
Key Words: p-Laplace; Free boundary; Approximation of solutions.