Inequalities between Dirichlet and Neumann eigenvalues of the polyharmonic operators

Provenzano, Luigi

doi:10.1090/proc/14615

Inequalities between Dirichlet and Neumann eigenvalues of the polyharmonic operators
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by Luigi Provenzano PDF

Proc. Amer. Math. Soc. 147 (2019), 4813-4821 Request permission

Abstract:

We prove that $\mu _{k+m}^m <\lambda _k^m$, where $\mu _k^m$ ($\lambda _k^m$) are the eigenvalues of $(-\Delta )^m$ on $\Omega \subset \mathbb R^d$, $d\geq 2$, with Neumann (Dirichlet) boundary conditions.

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