Electron. J. Diff. Eqns. Vol. 1995(1995), No. 08, pp. 1-20.

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

A. Acker & R. Meyer

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 < infinity. In addition, we prove the existence of a classical solution in N dimensions when p = 2 and, for 1 < p < infinity, 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 < infinity 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.

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A. Acker
Dept. of Mathematics and Statistics, Wichita State University
Wichita, KS 67260-0033, USA
e-mail: acker@twsuvm.uc.twsu.edu

R. Meyer
Dept. of Mathematics and Statistics, Northwest Missouri State University
Maryville, MO 64468. USA
e-mail: 0100745@northwest.missouri.edu

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