On the Traction Problem for the Lamé System on Curvilinear Polygons
Irina Mitrea · Journal of Integral Equations and Applications · 2004
We give a complete description of the spectra of certain elastostatic and hydrostatic boundary layer potentials in L p , 1 < p < ∞, on bounded curvilinear polygons.In particular, our analysis shows that the spectral radii of these operators on L p are less than one if p is large enough.This holds for the case of the boundary layer potential operator associated to the traction conormal derivative.Such results are important when dealing with the issue of constructively solving boundary value problems for the Lamé system of elasticity and for the Stokes system of hydrostatic in domains with isolated singularities.Our approach is based on Mellin transform techniques and Calderón-Zygmund theory.