Spectral properties of the layer potentials associated with elasticity equations and transmission problems on Lipschitz domains

We study the invertibility of βI+K and βI+K′ in L2(∂Ω) for where K,K′ are double layer potentials related to elasticity equations and Ω is bounded Lipschitz domain in Rn. Consequently, the spectrum on real line lies in . Applications to transmission problems are also presented.