Michiaki Onodera - Dynamical approach to an overdetermined problem II

This is the second part of the minicourse by Michiaki Onodera, Tokiotech.

Monday, Dec 09, 3pm-5pm: Thackeray 427

Tuesday, Dec 10, 10am-12pm, Thackeray 625

Tuesday, December 10, 2019 - 10:00 to 12:00
Speaker Information
Michiaki Onodera
Tokio Institute of Technology

Abstract or Additional Information

I will present a dynamical approach to an elliptic overdetermined problem, in which one seeks a bounded domain allowing a solution to an elliptic equation with both Dirichlet and Neumann boundary conditions.
One of the key observations is that the deformation of a continuously varying domain for a parametrized overdetermined problem forms a parabolic semiflow.
In particular, by this approach we can establish a rigidity and stability result for an overdetermined problem even in an asymmetric situation. 
Another application is the construction of a foliated family of solutions to Bernoulli's free boundary problem.