Scattering from infinite rough tubular surfaces

We study the Helmholtz equation in the exterior of an infinite perturbed cylinder with a Dirichlet boundary condition. Existence and uniqueness of solutions are established using the variational technique introduced (SIAM J. Math. Anal. 2005; 37(2):598-618). We also provide stability estimates with explicit dependence of the constants in terms of the frequency and the perturbed cylinder thickness.