On the first eigenvalue of the Dirichlet-to-Neumann operator on forms |
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Authors: | S Raulot A Savo |
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Institution: | 1. Laboratoire de Mathématiques R. Salem, UMR 6085 CNRS-Université de Rouen, Avenue de l?Université, BP.12, Technopôle du Madrillet, 76801 Saint-Étienne-du-Rouvray, France;2. Dipartimento SBAI, Sezione di Matematica, Sapienza Università di Roma, Via Antonio Scarpa 16, 00161 Roma, Italy |
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Abstract: | 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 Dirichlet-to-Neumann (or 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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