Brasco L, Pratelli A (2012)
Publication Status: Published
Publication Type: Journal article
Publication year: 2012
Publisher: Springer Verlag (Germany)
Book Volume: 22
Pages Range: 107-135
Journal Issue: 1
DOI: 10.1007/s00039-012-0148-9
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.
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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