Sharp Stability of Some Spectral Inequalities

Brasco L, Pratelli A (2012)

Publication Status: Published

Publication Type: Journal article

Publication year: 2012

Journal

Geometric and Functional Analysis Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 22

Pages Range: 107-135

Journal Issue: 1

DOI: 10.1007/s00039-012-0148-9

Abstract

In this work we review two classical isoperimetric inequalities involving eigenvalues of the Laplacian, both with Dirichlet and Neumann boundary conditions. The first one is classically attributed to Krahn and P. Szego and asserts that among sets of given measure, the disjoint union of two balls with the same radius minimizes the second eigenvalue of the Dirichlet-Laplacian, while the second one is due to G. SzegA and Weinberger and deals with the maximization of the first non-trivial eigenvalue of the Neumann-Laplacian. New stability estimates are provided for both of them.

Authors with CRIS profile

Aldo Pratelli

Involved external institutions

Università degli Studi di Pavia IT Italy (IT) Aix-Marseille University / Aix-Marseille Université FR France (FR)

How to cite

APA:

Brasco, L., & Pratelli, A. (2012). Sharp Stability of Some Spectral Inequalities. Geometric and Functional Analysis, 22(1), 107-135. https://dx.doi.org/10.1007/s00039-012-0148-9

MLA:

Brasco, Lorenzo, and Aldo Pratelli. "Sharp Stability of Some Spectral Inequalities." Geometric and Functional Analysis 22.1 (2012): 107-135.

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