JournalsifbVol. 9 , No. 3DOI 10.4171/ifb/169

Some geometric and analytic properties of solutions of Bernoulli free-boundary problems

  • Eugen Varvaruca

    University of Bath, United Kingdom
Some geometric and analytic properties of solutions of Bernoulli free-boundary problems cover

Abstract

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 function. Also investigated are convexity and monotonicity properties of free boundaries. In addition, we obtain some optimal estimates on the gradient of the harmonic function in question.