An isoperimetric inequality for the second eigenvalue of the Laplacian with Robin boundary conditions

Kennedy, James

doi:10.1090/S0002-9939-08-09704-9

An isoperimetric inequality for the second eigenvalue of the Laplacian with Robin boundary conditions
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by James Kennedy

Proc. Amer. Math. Soc. 137 (2009), 627-633

DOI: https://doi.org/10.1090/S0002-9939-08-09704-9

Published electronically: October 8, 2008

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Abstract:

We prove that the second eigenvalue of the Laplacian with Robin boundary conditions is minimized among all bounded Lipschitz domains of fixed volume by the domain consisting of the disjoint union of two balls of equal volume.

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