Biharmonic Steklov operator on differential forms

2022/06/10 by Chami, Fida El, Ginoux, Nicolas, Habib, Georges +1 · 2 citations
#53C21 #58C40 #58J32 #58J50 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2206.04914

Abstract

We introduce the biharmonic Steklov problem on differential forms by considering suitable boundary conditions. We characterize its smallest eigenvalue and prove elementary properties of the spectrum. We obtain various estimates for the first eigenvalue, some of which involve eigenvalues of other problems such as the Dirichlet, Neumann, Robin and Steklov ones. Independently, new inequalities relating the eigenvalues of the latter problems are proved.

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• Integral Formulas for Differential Forms on Weighted Manifolds and Applications
• Biharmonic Steklov problems with Neumann boundary conditions and spectral inequalities on differential forms

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