Abstract
In this paper we prove that the L2 spectral radius of the traction double layer potential operator associated with the Lamé system on an infinite sector in R2 is within 10-2 from a certain conjectured value which depends explicitly on the aperture of the sector and the Lamé moduli of the system. This type of result is relevant to the spectral radius conjecture, cf., e.g., Problem 3.2.12 in [C.E. Kenig, Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems, CBMS Reg. Conf. Ser. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1994]. The techniques employed in the paper are a blend of classical tools such as Mellin transforms, and Calderón-Zygmund theory, as well as interval analysis-resulting in a computer-aided proof.
Original language | English |
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Pages (from-to) | 181-198 |
Number of pages | 18 |
Journal | Journal of Differential Equations |
Volume | 233 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Feb 2007 |
Externally published | Yes |
Keywords
- Computer-aided proof
- Interval analysis
- Lamé system
- Layer potentials
- Spectral radius
- Traction conormal derivative