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2003 Some counterexamples for the spectral-radius conjecture
Irina Mitrea, Warwick Tucker
Differential Integral Equations 16(12): 1409-1439 (2003).

Abstract

The goal of this paper is to produce a series of counterexamples for the $L^p$ spectral radius conjecture, $1 <p <\infty$, for double-layer potential operators associated to a distinguished class of elliptic systems in polygonal domains in $\mathbb R^2$. More specifically the class under discussion is that of second-order elliptic systems in two dimensions whose coefficient tensor (with constant real entries) is symmetric and strictly positive definite. The general techniques employed are those of the Mellin transform and Calderón-Zygmund theory. For the case $p\in(1,4)$, we construct a computer-aided proof utilizing validated numerics based on interval analysis.

Citation

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Irina Mitrea. Warwick Tucker. "Some counterexamples for the spectral-radius conjecture." Differential Integral Equations 16 (12) 1409 - 1439, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1073.45500
MathSciNet: MR2029908

Subjects:
Primary: 45E05
Secondary: 31A15, 35J25, ‎45P05‎, 47A10, 47G10

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 12 • 2003
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