On the Dirichlet problem for the dissipative Helmholtz equation in the exterior of non-closed Lipschitz surfaces

The Dirichlet problem for the dissipative Helmholtz equation is considered in the exterior of non-closed Lipschitz surfaces in R³. Theorems on existence and uniqueness of a weak solution of the problem are proved. The problem is reduced to a uniquely solvable integral equation. The integral representation of a weak solution is obtained.