Interval Analysis Techniques for Boundary Value Problems of Elasticity in Two Dimensions
2007 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 233, no 1, 181-198 p.Article in journal (Refereed) Published
In this paper we prove that the L-2 spectral radius of the traction double layer potential operator associated with the Lame system on an infinite sector in R-2 is within 10(-2) from a certain conjectured value which depends explicitly on the aperture of the sector and the Lame 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 Calderon-Zygmund theory, as well as interval analysis-resulting in a computer-aided proof.
Place, publisher, year, edition, pages
2007. Vol. 233, no 1, 181-198 p.
Lamé system, Layer potentials, Traction conormal derivative, Spectral radius, Interval analysis, Computer-aided proof
IdentifiersURN: urn:nbn:se:uu:diva-22535DOI: 10.1016/j.jde.2006.10.010ISI: 000244159900008OAI: oai:DiVA.org:uu-22535DiVA: diva2:50308