Biharmonic Steklov problems with Neumann boundary conditions and spectral inequalities on differential forms

Abstract: We introduce three biharmonic Steklov problems on differential forms with Neumann boundary conditions and show that they are elliptic. We prove the existence of a discrete spectrum for each of those problems and give associated variational characterizations for their eigenvalues. We establish eigenvalue estimates known as Kuttler-Sigillito inequalities, relating the eigenvalues of these problems with the eigenvalues of the Steklov, Dirichlet and Neumann standard problems as well as the biharmonic Steklov problem with Dirichlet boundary conditions on differential forms.