Special Minicourse Lecture 2 - Dynamical Approach to an Overdetermined Problem


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.

The talks will be accessible to graduate students with a good basis in Analysis and PDE.

December 10, 2019 - 10:00am to 12:00pm

Location and Address

625 Thackeray Hall

Speaker Information

Michiaki Onodera, Tokyo Institute of Technology