Electron. J. Diff. Eqns., Vol. 2006(2006), No. 128, pp. 1-23.

Existence of solutions for the one-phase and the multi-layer free-boundary problems with the p-laplacian operator

Idrissa Ly, Diaraf Seck

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.

Submitted March 6, 2006. Published October 11, 2006.
Math Subject Classifications: 35R35.
Key Words: Bernoulli free boundary problem; starshaped domain; shape optimization; shape derivative; monotonicity.

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Idrissa Ly
Faculté des Sciences Economiques et de Gestion
Université Cheikh Anta Diop
B.P 5683, Dakar, Sénégal
email: ndirkaly@ugb.sn
Diaraf Seck
Faculté des Sciences Economiques et de Gestion
Université Cheikh Anta Diop
B.P 5683, Dakar, Sénégal
email: dseck@ucad.sn

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