Special Session 73: Nonlinear elliptic and parabolic equations and related functional inequalities

Concentrations in Bernoulli`s free boundary problem

Michiaki Onodera
Tokyo Institute of Technology
Japan
Co-Author(s):    
Abstract:
Bernoulli`s free boundary problem is an overdetermined boundary value problem in which one seeks an annular domain such that the capacitary potential satisfies an extra boundary condition. I will talk about recent progress on a conjecture of Flucher and Rumpf that asserts the existence of a family of free boundaries concentrating at non-degenerate local minima of the Robin function.