Joint BCAM-UPV/EHU Analysis and PDE seminar: Friedlander comparison theorem for the eigenvalues of the Stokes operator

Abstract
We prove a comparison theorem for the eigenvalues of the Dirichlet and Neu mann Stokes operators: Let AN and AD be the Neumann Stokes operator and Dirichlet Stokes operator. respectively, and let λN1 ≤ λN2 ≤ . . . and λD1 ≤ λD2 ≤ . . . be the eigenvalues of AN and AD repeated with multiplicity, respectively. Then 
λNn+1 < λDn
for all n ∈ N.
There is a simple relation between the eigenvalues of the Stokes operator with Robin boundary conditions and the Dirichlet-to-Neumann operator associated with the Stokes operator. Using results by ter Elst and Arendt on Dirichlet-to Neumann graphs to avoid any issues when the Dirichlet-to-Neumann operator is ill-defined, we study the flow of the eigenvalues between the Stokes-Dirichlet and Stokes-Neumann operators, allowing us to prove that the eigenvalue estimate holds if the Dirichlet-to-Neumann graph has a negative eigenvalue.

From joint work with Tom ter Elst (Auckland University)


Link to the session: https://zoom.us/j/92567527168?pwd=d0F4NXhKVk9YVmlIZ0Noem84VnBUQT09


More info at https://sites.google.com/view/apdebilbao/home