Berezin--Li--Yau inequalities on domains on the sphere

Alexei Ilyin; Ari Laptev

Berezin--Li--Yau inequalities on domains on the sphere

Spectral Theory 2018-01-01 v1

Authors: Alexei Ilyin , Ari Laptev

Abstract

We prove Berezin--Li--Yau inequalities for the Dirichlet and Neumann eigenvalues on domains on the sphere $\mathbb{S}^{d-1}$ . The case of $\mathbb{S}^{2}$ is treated in greater detail, including the vector Dirichlet Laplacian and the Stokes operator.

Keywords

berezin-li-yau inequalities dirichlet eigenvalues neumann eigenvalues sphere stokes operator vector laplacian

Cite

@article{arxiv.1712.10078,
  title  = {Berezin--Li--Yau inequalities on domains on the sphere},
  author = {Alexei Ilyin and Ari Laptev},
  journal= {arXiv preprint arXiv:1712.10078},
  year   = {2018}
}

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