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Article Dans Une Revue Journal of Functional Analysis Année : 2012

On the first eigenvalue of the Dirichlet-to-Neumann operator on forms

Résumé

We study a Dirichlet-to-Neumann eigenvalue problem for differential forms on a compact Riemannian manifold with smooth boundary. This problem is a natural generalization of the classical Steklov problem on functions. We derive a number of upper and lower bounds for the first eigenvalue in several contexts: many of these estimates will be sharp, and for some of them we characterize equality. We also relate these new eigenvalues with those of other operators, like the Hodge Laplacian or the biharmonic Steklov operator.
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Dates et versions

hal-00593140 , version 1 (13-05-2011)
hal-00593140 , version 2 (07-11-2011)

Identifiants

Citer

Simon Raulot, Alessandro Savo. On the first eigenvalue of the Dirichlet-to-Neumann operator on forms. Journal of Functional Analysis, 2012, 262 (3), pp.889-914. ⟨10.1016/j.jfa.2011.10.008⟩. ⟨hal-00593140v2⟩
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