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

TL;DR

This paper investigates the geometric behavior of the free boundary in a one-phase Bernoulli problem with mixed boundary conditions, showing that near the intersection point, the free boundary approaches at a right angle.

Contribution

It provides a new geometric insight into the free boundary behavior at the junction of different boundary conditions in Bernoulli problems.

Findings

Free boundary approaches the junction at a right angle.

Results apply to symmetric local minimizers.

Analysis enhances understanding of boundary interaction effects.

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 $\pi/2$