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

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

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

### 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 equaiton 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.