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A Payne-Weinberger eigenvalue estimate for wedge domains on spheres


Authors: Jesse Ratzkin and Andrejs Treibergs
Journal: Proc. Amer. Math. Soc. 137 (2009), 2299-2309
MSC (2000): Primary 35P15
DOI: https://doi.org/10.1090/S0002-9939-09-09790-1
Published electronically: March 3, 2009
MathSciNet review: 2495263
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Abstract: A Faber-Krahn type argument gives a sharp lower estimate for the first Dirichlet eigenvalue for subdomains of wedge domains in spheres, generalizing the inequality for the plane, found by Payne and Weinberger. An application is an alternative proof to the finiteness of a Brownian motion capture-time estimate.


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Additional Information

Jesse Ratzkin
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Address at time of publication: School of Mathematical Sciences, Aras Na Laoi, University College Cork, Cork, Ireland
Email: J.Ratzkin@ucc.ie

Andrejs Treibergs
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: treiberg@math.utah.edu

DOI: https://doi.org/10.1090/S0002-9939-09-09790-1
Received by editor(s): April 10, 2008
Published electronically: March 3, 2009
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.