On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain
Simon Raulot, Alessandro Savo · arXiv (Cornell University) · 2012
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 ${\rm Vol}(\bdΩ)/{\rm Vol}(Ω)$.