On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain

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Abstract

We compute the whole spectrum of the Dirichlet-to-Neumann operator acting on differential p-forms on the unit Euclidean ball. Then, we prove a new upper bound for its first eigenvalue on a domain Ω in Euclidean space in terms of the isoperimetric ratio V ol (∂Ω) / V ol (Ω). © 2013 Elsevier B.V.

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Raulot, S., & Savo, A. (2014). On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain. Journal of Geometry and Physics, 77, 1–12. https://doi.org/10.1016/j.geomphys.2013.11.002

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