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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: James Kennedy
Journal: Proc. Amer. Math. Soc. 137 (2009), 627-633
MSC (2000): Primary 35P15, 35J25
Published electronically: October 8, 2008
MathSciNet review: 2448584
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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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Additional Information

James Kennedy
Affiliation: School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
Email: J.Kennedy@maths.usyd.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09704-9
PII: S 0002-9939(08)09704-9
Keywords: Isoperimetric inequality, Laplacian, Robin boundary conditions, elastically supported membrane
Received by editor(s): January 30, 2008
Published electronically: October 8, 2008
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.