Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues

Pier Domenico Lamberti; Luigi Provenzano

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arXiv · 1410.0517

Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues

Pier Domenico Lamberti·Luigi Provenzano

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Abstract

We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of boundary mass concentration. We discuss the asymptotic behavior of the Neumann eigenvalues in a ball and we deduce that the Steklov eigenvalues minimize the Neumann eigenvalues. Moreover, we study the dependence of the eigenvalues of the Steklov problem upon perturbation of the mass density and show that the Steklov eigenvalues violates a maximum principle in spectral optimization problems.

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BibTeX RIS

Pier Domenico Lamberti, Luigi Provenzano. 2014-10-02. Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues. https://arxiv.org/abs/1410.0517

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