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2008 $L^p$ Spectral Radius Estimates for the Lamé System on an Infinite Sector
Tomas Johnson
Experiment. Math. 17(3): 333-339 (2008).

Abstract

We prove, using interval analysis methods, that the $L^2$, $L^4$, and $L^8$ spectral radii of the traction double layer potential operator associated with the Lam\'e system on an infinite sector in $\mathbb R}^2$ are within $2.5 x 10^-3$, $10^-2$, and $10^-2$, respectively, from a certain conjectured value that depends explicitly on the aperture of the sector and the Lamé moduli of the system. We also indicate how to extend these results to $L^p$ for entire intervals of $p$, $p\geq2$.

Citation

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Tomas Johnson. "$L^p$ Spectral Radius Estimates for the Lamé System on an Infinite Sector." Experiment. Math. 17 (3) 333 - 339, 2008.

Information

Published: 2008
First available in Project Euclid: 19 November 2008

zbMATH: 1161.35364
MathSciNet: MR2455704

Subjects:
Primary: 35J25 , 47-04
Secondary: 45E05 , 65G20

Keywords: computer-aided proof , interval analysis , Lamé system , spectral radius , traction conormal derivative

Rights: Copyright © 2008 A K Peters, Ltd.

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