Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 102, pp. 1-16.

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

Authors: Pierre Cardaliaguet (Univ. de Bretagne Occidentale, France)
         Rabah Tahraoui (Univ. Paris IX Dauphine, France)
         
Abstract: 
  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.