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.

Show me the
PDF file (250 KB),
TEX file, and other files for this article.

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

Return to the EJDE home page.