Electron. J. Diff. Eqns., Vol. 2004(2004), No. 109, pp. 1-12

Isoperimetric inequality for an interior free boundary problem with p-laplacian operator

Idrissa Ly, Diaraf Seck

Abstract:
By considering the p-Laplacian operator, we establish an existence and regularity result for a shape optimization problem. From a monotony result, we show the existence of a solution to the interior problem with a free surface for a family of Bernoulli constants. We also give an optimal estimation for the upper bound of the Bernoulli constant.

Submitted April 7, 2004. Published September 14, 2004.
Math Subject Classifications: 35R35.
Key Words: Bernoulli free boundary problem; starshaped domain; shape optimization; shape derivative; monotony.

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

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