Mikhajlov, S. E. On an integral equation of some boundary value problems for harmonic functions in plane multiply connected domains with nonregular boundary. (English. Russian original) Zbl 0545.31003 Math. USSR, Sb. 49, 525-536 (1984); translation from Mat. Sb., Nov. Ser. 121(163), No. 4, 533-544 (1983). Let D be a bounded or an unbounded region in the plane whose boundary \(\Gamma\) consists of finitely many curves of bounded rotation without cusps (but with corner points). The Dirichlet problem and the oblique derivative problem (an analog of the Neumann problem) on D is solved. Using the angular potential and a generalized logarithmic potential, respectively, the mentioned problems lead to Fredholm integral equations on \(\Gamma\). These equations are studied in detail, the Fredholm radius of these equations in the spaces \(L_ p\) is evaluated, and it is shown under which conditions the solutions of these equations can be expressed by Neumann series. Reviewer: M.Dont Cited in 2 Documents MSC: 31A25 Boundary value and inverse problems for harmonic functions in two dimensions 31A10 Integral representations, integral operators, integral equations methods in two dimensions 45B05 Fredholm integral equations Keywords:multiply connected domains; integral equations method; cusps; corner points; Dirichlet problem; oblique derivative; angular potential; logarithmic potential; Fredholm integral equations; Fredholm radius; Neumann series PDFBibTeX XMLCite \textit{S. E. Mikhajlov}, Math. USSR, Sb. 49, 525--536 (1984; Zbl 0545.31003); translation from Mat. Sb., Nov. Ser. 121(163), No. 4, 533--544 (1983) Full Text: DOI EuDML