Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 128, pp. 1-23.

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

Authors: Idrissa Ly   (Univ. Cheikh Anta Diop, Senegal)
         Diaraf  Seck (Univ. Cheikh Anta Diop, Senegal)

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.