Some counterexamples for the spectral-radius conjecture

Irina Mitrea, Warwick Tucker

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The goal of this paper is to produce a series of counterexamples for the Lp spectral radius conjecture, 1<p<∞, for double-layer potential operators associated to a distinguished class of elliptic systems in polygonal domains in R2. 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∈(1,4), we construct a computer-aided proof utilizing validated numerics based on interval analysis.
Original languageEnglish
Pages (from-to)1409-1439
Number of pages31
JournalDifferential and Integral Equations
Issue number12
Publication statusPublished - Dec 2003
Externally publishedYes

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