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 M~2. More specifically the class under discussion is that of second-order elliptic systems in two dimensions whose coeffi-cient tensor (with constant real entries) is symmetric and strictly posi-tive definite. The general techniques employed are those of the Mellin transform and Calderon-Zygnumd theory. For the case p ∈ (1,4), we construct a computer-aided proof utilizing validated numerics based on interval analysis.
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