Electron. J. Diff. Eqns., Vol. 2002(2002), No. 102, pp. 1-16.

Some uniqueness results for Bernoulli interior free-boundary problems in convex domains

Pierre Cardaliaguet & Rabah Tahraoui

We establish the existence of a elliptic family of convex solutions for Bernoulli interior free-boundary problems in bounded convex domains. We also proved that there is a unique solution to the problem associated with the so-called Bernoulli constant, and give an estimate from above for this constant.

Submitted January 3, 2002. Published December 10, 2002.
Math Subject Classifications: 35R35.
Key Words: Bernoulli free-boundary problem, convex solutions, Borell's inequality.

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  Pierre Cardaliaguet
Universite de Bretagne Occidentale, Departement de Mathematiques,
6, avenue Victor-le-Gorgeu,
B.P. 809, 29285 Brest Cedex, France
e-mail: Pierre.Cardaliaguet@univ-brest.fr
Rabah Tahraoui
C.E.R.E.M.A.D.E., Universite Paris IX Dauphine,
Place du Marechal de Lattre de Tassigny, 75775 Paris Cedex 16 France
I.U.F.M. de Rouen, 2, rue du Tronquet, B.P. 18,
Mont Saint-Aignan 76131 France
e-mail: tahraoui@ceremade.dauphine.fr

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