L^p Spectral Radius Estimates for the Lamé System on an Infinite Sector

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 Lamé system on an infinite sector in ℝ² are within 2.5 × 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 ≥ 2.

Keywords:

• Primary 35J25, 47-04
• Secondary 45E05, 65G20
• Lamé system
• traction conormal derivative
• spectral radius
• interval analysis
• computer-aided proof