The Dirichlet problem for the dissipative Helmholtz equation in a plane domain bounded by closed and open curves
The author studies the title problem in an arbitrary plane domain (internal or external) bounded by a finite number of sufficiently smooth closed and open curves, including cuts. After reducing the problem to a Fredholm equation of second kind, he establishes the existence and uniqueness of classical solution. The proof uses essentially the methods of potential theory.
scientific article; zbMATH DE number 1180295