A note on the ellipticity of the single layer potential in two-dimensional linear elastostatics (Q596686)

It is well-known that in the case of two-dimensional Laplace operator the corresponding single layer potential of the Laplace operator is \(H^{-1/2}(\Gamma)\)-elliptic, if the domain \(\Omega\) satisfies the scaling condition \(\operatorname{diam} \Omega<1\). In the case of the system of planar linear elastostatics it seems to be an open problem, how to scale the computational domain \(\Omega\) to ensure the \([H^{-1/2}(\Gamma)]^2\)-ellipticity of the single layer potential \(V\). In this note the author applies the ideas of the proof for the single layer potential of the Laplace operator to show the ellipticity of the single layer potential \(V\) if a suitable scaling of the computational domain \(\Omega\) is applied.