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A Payne-Weinberger eigenvalue estimate for wedge domains on spheres
Author(s):
Jesse
Ratzkin;
Andrejs
Treibergs
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2299-2309.
MSC (2000):
Primary 35P15
Posted:
March 3, 2009
MathSciNet review:
2495263
Retrieve article in:
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Abstract |
References |
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Additional information
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.
References:
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- [Ch]
- I. Chavel, Eigenvalues in Riemannian Geometry. In Pure and Applied Mathematics, 115. Academic Press, Inc., Orlando, FL, 1984. MR 768584 (86g:58140)
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 of Brownian motion. Prob. Theory and Rel. Fields 74 (1987), 1-29. MR 863716 (88d:60205) - [F]
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- [K]
- E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises. Math. Ann. 94 (1925), 97-100. MR 1512244
- [LT]
- P. Li and A. Treibergs, Applications of eigenvalue techniques to geometry. Contemporary Geometry: J.-Q. Zhong Memorial Volume (H.-H. Wu, ed.). University Series in Mathematics, Plenum Press, New York, 1991, pp. 22-54. MR 1170358 (93i:58159)
- [LS]
- W. Li and Q.-M. Shao, Capture time of Brownian pursuits. Prob. Theory and Rel. Fields 121 (2001), 30-48. MR 1857107 (2002h:60173)
- [P]
- L. Payne, Isoperimetric inequalities and their applications. SIAM Review 9 (1967), 453-488. MR 0218975 (36:2058)
- [PW]
- L. Payne and H. Weinberger, A Faber-Krahn inequality for wedge-like membranes. Journal of Mathematics and Physics 39 (1960), 182-188. MR 0128158 (23:B1202)
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- J. Ratzkin and A. Treibergs, A capture problem in Brownian motion and eigenvalues of spherical domains. Trans. Amer. Math. Soc., 361 (2009), 391-405.
- [Sz]
- G. Szegő, Über eine Verallgemeinerung des Dirichletschen Integrals. Math. Zeit. 52 (1950), 676-685. MR 0040493 (12:703c)
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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:
10.1090/S0002-9939-09-09790-1
PII:
S 0002-9939(09)09790-1
Received by editor(s):
April 10, 2008
Posted:
March 3, 2009
Communicated by:
Chuu-Lian Terng
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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