The mixed problem for the Lamé system in a class of Lipschitz domains

We consider the mixed problem for the Lamé system{(L u = 0, in Ω,; u |_D = f_D, on D,; frac(∂ u, ∂ ρ) = f_N, on N,; (∇ u)^* ∈ L^p (∂ Ω)) in the class of bounded Lipschitz creased domains. Here D and N partition ∂Ω and ∂ / ∂ ρ stands for the traction operator. We suppose the Dirichlet data f_D has one derivative in L^p (D) and the traction data f_N is in L^p (N). For p in a small interval containing 2, we find a unique solution to the mixed problem subject to the condition that the non-tangential maximal function of the gradient of the solution is in L^p (∂ Ω).