arXiv subjects

Rodolphe Abou Assali

Publications and source records attributed to Rodolphe Abou Assali.

2 recordsLinked to original sources

arXiv2026

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

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.

math.DG↗

arXiv2026

Geometric eigenvalue estimates of Kuttler-Sigillito type on differential forms

We introduce a new biharmonic Steklov problem on differential forms with Dirichlet-type boundary conditions and show that it is elliptic. We prove the existence of a discrete spectrum for this problem and give variational characterizations for eigenvalues associated to it. We establish eigenvalue estimates known as Kuttler-Sigillito inequalities, that connect the eigenvalues of different problems on differential forms with curvature quantities on the manifold.

math.DG↗