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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Acknowledgements
We acknowledge financial support by the research project “Singular perturbation problems for differential operators”, Progetto di Ateneo of the University of Padova.
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Lamberti, P.D., Provenzano, L. (2015). Viewing the Steklov Eigenvalues of the Laplace Operator as Critical Neumann Eigenvalues. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_21
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DOI: https://doi.org/10.1007/978-3-319-12577-0_21
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-12576-3
Online ISBN: 978-3-319-12577-0
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