Abstract
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.
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Part of this work is supported by an NZ-EU IRSES counterpart fund and the Marsden Fund Council from Government funding, administered by the Royal Society of New Zealand. Part of this work is supported by the EU Marie Curie IRSES program, Project ‘AOS’, No. 318910.
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Arendt, W., ter Elst, A.F.M. Ultracontractivity and Eigenvalues: Weyl’s Law for the Dirichlet-to-Neumann Operator. Integr. Equ. Oper. Theory 88, 65–89 (2017). https://doi.org/10.1007/s00020-017-2353-2
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DOI: https://doi.org/10.1007/s00020-017-2353-2