Interval analysis techniques for boundary value problems of elasticity in two dimensions

摘要: In this paper we prove that the L-2 spectral radius of traction double layer potential operator associated with Lame system on an infinite sector in R-2 is within 10(-2) from a certain conjectured value which depends explicitly aperture and moduli system. This type result relevant to conjecture, cf., e.g., Problem 3.2.12 [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 are blend classical tools such as Mellin transforms, Calderon-Zygmund theory, well interval analysis-resulting computer-aided proof.