On the behavior of the free boundary for a one-phase Bernoulli problem with mixed boundary conditions

Abstract

This paper is concerned with the study of the behavior of the free boundary for a class of solutions to a one-phase Bernoulli free boundary problem with mixed periodic-Dirichlet boundary conditions. It is shown that if the free boundary of a symmetric local minimizer approaches the point where the two different conditions meet, then it must do so at an angle of $\pi /2$

28 pages, 3 figures