Solvability of static contact problems with Coulomb friction for orthotropic material

We calculate an exact upper bound for the magnitude of the coefficient of friction that ensures the existence of a solution to a static contact problem with Coulomb friction. The approach is based on a general existence result that is valid under the assumption that the coefficient of friction is bounded by a certain constant depending on the constants in two special trace type estimates for a half space domain. We calculate these constants for orthotropic material and two space dimensions with the help of a representation for a partial Fourier transform of the solution to the corresponding system of elasticity equations. The result is compared to the formula for general anisotropic material. The new bound for orthotropic material is significantly larger than the old one for general material, if the material is close to an isotropic material with Poisson ration greater than zero. For some cases the new bound can be even larger than one.