Chiu-Yen Kao's Abstract


Claremont Mathematics Weekend


Sponsored by Claremont Colleges


January 30 - 31, 2016


Speaker: Chiu-Yen Kao
Title: Computational Methods for Extremal Steklov Problems

We develop a computational method for extremal Steklov eigenvalue problems and apply it to study the problem of maximizing the p-th Steklov eigenvalue as a function of the domain with a volume constraint. In contrast to the optimal domains for several other extremal Dirichlet- and Neumann-Laplacian eigenvalue problems, computational results suggest that the optimal domains for this problem are very structured. We reach the conjecture that the domain maximizing the p-th Steklov eigenvalue is unique (up to dilations and rigid transformations), has p-fold symmetry, and an axis of symmetry. The p-th Steklov eigenvalue has multiplicity 2 if p is even and multiplicity 3 if p>=3 is odd.