Some geometric and analytic properties of solutions of Bernoulli free-boundary problems
Some geometric and analytic properties of solutions of Bernoulli free-boundary problems
A Bernoulli free-boundary problem is one of finding domains in the plane on which a harmonic function simultaneously satisfies linear homogeneous Dirichlet and inhomogeneous Neumann boundary conditions. For a general class of Bernoulli problems, we prove that any free boundary, possibly with many singularities, is necessarily the graph of a …