A Free Boundary Problem for the p-Laplacian: Uniqueness, Convexity, and Successive Approximation of Solutions
Date
1995-06-21
Authors
Acker, Andrew F.
Meyer, R.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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 < ∞. In addition, we prove the existence of a classical solution in N dimensions when p = 2 and, for 1 < p < ∞, 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 < ∞) that the free boundary is convex when the fixed boundary is convex.
Description
Keywords
p-Laplace, Free boundary, Approximation of solutions
Citation
Acker, A. & Meyer, R. (1995). A free boundary problem for the p-Laplace: uniqueness, convexity, and successive approximation of solutions. <i>Electronic Journal of Differential Equations, 1995</i>(08), pp. 1-20.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.