Krutitskii, P. A. The Neumann problem in a plane domain bounded by closed and open curves. (English) Zbl 0982.31001 Complex Variables, Theory Appl. 38, No. 1, 1-20 (1999). The Neumann problem for the Laplace equation in a connected plane region bounded by closed and open curves is studied. The existence of a classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable. Reviewer: P.A.Krutitskii (Moskva) Cited in 3 Documents MSC: 31A10 Integral representations, integral operators, integral equations methods in two dimensions 31A05 Harmonic, subharmonic, superharmonic functions in two dimensions 35J25 Boundary value problems for second-order elliptic equations Keywords:harmonic functions; Neumann problem; boundary integral equation method; cracks; screens; wrings PDFBibTeX XMLCite \textit{P. A. Krutitskii}, Complex Variables, Theory Appl. 38, No. 1, 1--20 (1999; Zbl 0982.31001) Full Text: DOI