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arXiv · 1202.3605

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

Simon Raulot·Alessandro Savo
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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 $\Omega$ in Euclidean space in terms of the isoperimetric ratio ${\rm Vol}(\bd\Omega)/{\rm Vol}(\Omega)$.

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Simon Raulot, Alessandro Savo. 2012-02-16. On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain. https://arxiv.org/abs/1202.3605

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