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

Irina Mitrea, Warwick Tucker

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3 Citations (Scopus)


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 languageEnglish
Pages (from-to)181-198
Number of pages18
JournalJournal of Differential Equations
Issue number1
Publication statusPublished - 1 Feb 2007
Externally publishedYes


  • Computer-aided proof
  • Interval analysis
  • Lamé system
  • Layer potentials
  • Spectral radius
  • Traction conormal derivative

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