Mixed boundary value problem of Laplace equation in a bounded Lipschitz domain

We study the existence and uniqueness of the mixed boundary value problem for Laplace equation in a bounded Lipschitz domain Ω⊂Rn, n⩾3. Let the boundary ∂Ω of Ω be decomposed by , Γ1∩Γ2=∅. We will show that if the Neumann data ψ is in and the Dirichlet data f is in , then the mixed boundary value problem has a unique solution and the solution is represented by potentials.