On the Green function of an orthotropic clamped plate in a half-plane

First, we calculate, in a heuristic manner, the Green function of an orthotropic plate in a half-plane which is clamped along the boundary. We then justify the solution and generalize our approach to operators of the form (Q(partial derivative') - a(2)partial derivative(2)(n))(Q(partial derivative') - b(2)partial derivative(2)(n)) (where partial derivative' = (partial derivative(1), ... , partial derivative(n-1)) and a > 0, b > 0, a not equal b) with respect to Dirichlet boundary conditions at x(n) = 0. The Green function G(xi) is represented by a linear combination of fundamental solutions E-c of Q(partial derivative')(Q(partial derivative') - c(2)partial derivative(2)(n)), c is an element of {a, b}, that are shifted to the source point xi, to the mirror point -xi, and to the two additional points - a/b xi and - b/a xi, respectively.