The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves. (English) Zbl 0910.35040

Author’s abstract: The Neumann problem for the dissipative Helmholtz equation in a connected plane region bounded by closed and open curves is studied. Existence of classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable. Our approach holds for both internal and external domains.


35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
31A25 Boundary value and inverse problems for harmonic functions in two dimensions
35J25 Boundary value problems for second-order elliptic equations
Full Text: DOI EuDML