Maria del Mar Gonzalez

Universidad Autónoma de Madrid

A free boundary problem for the half-Laplacian, the Steklov eigenvalue and higher order generalizations

We consider the eigenvalue optimization for the composite membrane problem with fractional Laplacian, which is related to the Steklov eigenvalue. For this free boundary problem we will prove existence of solutions and study properties of the optimal configuration, including symmetry and symmetry breaking. This is joint work with K.-A. Lee and T. Lee. If time permits, I will consider higher order generalizations of the Steklov eigenvalue.