Krutitskii, P. A. The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves. (English) Zbl 0910.35040 Int. J. Math. Math. Sci. 21, No. 2, 209-216 (1998). 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. Reviewer: C.Y.Chan (Lafayette) Cited in 1 ReviewCited in 7 Documents MSC: 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 Keywords:existence of classical solution; Fredholm equation PDF BibTeX XML Cite \textit{P. A. Krutitskii}, Int. J. Math. Math. Sci. 21, No. 2, 209--216 (1998; Zbl 0910.35040) Full Text: DOI EuDML OpenURL