Existence of solutions for the one-phase and the multi-layer free-boundary problems with the p-laplacian operator
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Date
2006-10-11
Authors
Ly, Idrissa
Seck, Diaraf
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
By considering the p-laplacian operator, we show the existence of a solution to the exterior (resp interior) free boundary problem with non constant Bernoulli free boundary condition. In the second part of this article, we study the existence of solutions to the two-layer shape optimization problem. From a monotonicity result, we show the existence of classical solutions to the two-layer Bernoulli free-boundary problem with nonlinear joining conditions. Also we extend the existence result to the multi-layer case.
Description
Keywords
Bernoulli free boundary problem, Starshaped domain, Shape optimization, Shape derivative, Monotonicity
Citation
Ly, I., & Seck, D. (2006). Existence of solutions for the one-phase and the multi-layer free-boundary problems with the p-laplacian operator. <i>Electronic Journal of Differential Equations, 2006</i>(128), pp. 1-23.
Rights
Attribution 4.0 International