Interval analysis techniques for boundary value problems of elasticity in two dimensions
From the authors' abstract: It is proved that the \(L^2\) spectral radius of the traction double layer potential operator associated with the Lamé system on an infinite sector in \(\mathbb{R}^2\) 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 as described, e.g., as Problem 3.2.12 in the work by \textit{C. E. Kenig} [Harmonic analysis techniques for second order elliptic boundary value problems, CBMS Reg. Conf. Ser. Math. 83, Am. 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.
scientific article; zbMATH DE number 5124482
scientific article