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

Abstract

We introduce a biharmonic Steklov problem with Neumann-type boundary conditions on differential forms and show that it is well-posed. We prove the existence of a discrete spectrum for this problem and provide associated variational characterizations of its eigenvalues. We establish eigenvalue estimates known as Kuttler-Sigillito inequalities, relating the eigenvalues of this problem to those of the Steklov, Dirichlet and Neumann problems, as well as the biharmonic Steklov problem with Dirichlet boundary conditions on differential forms.