Some geometric and analytic properties of solutions of Bernoulli free-boundary problems
Eugen VarvarucaUniversity of Bath, United Kingdom
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.
Cite this article
Eugen Varvaruca, Some geometric and analytic properties of solutions of Bernoulli free-boundary problems. Interfaces Free Bound. 9 (2007), no. 3, pp. 367–381DOI 10.4171/IFB/169