Ultracontractivity and Eigenvalues: Weyl's Law for the Dirichlet-to-Neumann Operator

作者：Arendt W; ter Elst A F M^*

来源：Integral Equations and Operator Theory, 2017, 88(1): 65-89.

DOI：10.1007/s00020-017-2353-2

• Dirichlet-to-Neumann operator
• Weyl asymptotics
• Ultracontractivity

We show an interesting relation between ultracontractivity and Weyl asymptotics. Then both properties are studied for their behaviour with respect to perturbation. The results are used to establish Weyl's law for the Dirichlet-to-Neumann operator associated with -Delta+ V, where V is a measurable bounded potential. In particular, we show that its eigenvalues determine the surface area of the domain.

• 出版日期2017-5