Bernoulli Free-boundary Problems

Establishes an equivalence between Bernoulli free boundary problems and a class of equations for real-valued functions of one real variable. The equivalent equations can be written as nonlinear Riemann-Hilbert problems and the theory of complex Hardy spaces in the unit disc has a central role. A canonical Morse index can be assigned to free boundaries and the Calculus of Variations becomes available as a tool for the study.