Special Session 65: Geometry of PDEs on Manifolds and Nilpotent Lie Groups

Concentration phenomena for Bernoulli`s free boundary problem
Michiaki Onodera
Institute of Science Tokyo
Japan
Co-Author(s):    
Abstract:
Bernoulli`s free boundary problem is an overdetermined boundary value problem in which one seeks an annular domain with a fixed exterior boundary and an interior free boundary, such that the associated capacitary potential also satisfies a prescribed Neumann boundary condition on the free boundary. I will talk about recent developments regarding to 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.