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arxiv: 1712.10078 · v1 · pith:CICPWK2Mnew · submitted 2017-12-28 · 🧮 math.SP

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

classification 🧮 math.SP
keywords berezin--li--yaudirichletdomainsinequalitiesmathbbspherecasedetail
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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.

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