On a Bernoulli problem with geometric constraints
Antoine Laurain, Yannick Privat (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by ≥ 0 and its boundary to contain a segment of the hyperplane { = 0} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness...