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

By S. Raulot, A. Savo. 2011

50 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/74c77fa0b82e995d8239f2c5e1417514f3043809

Citations in the corpus

• SPECTRAL GEOMETRY OF THE STEKLOV PROBLEM (2014, unknown): “Isoperimetric bounds for the first nonzero eigenvalue of the Dirichlet-to-Neumann operator on forms have been recently obtained in [93, 94].”