Abstract
The explicit solution of some axialsymmetric scalar screen problems in Sobolev spaces is presented. The well-posedness of the boundary integral equations, which are formulated as dual integral equations, is proved. A reduction for the mixed boundary value problem to a system of singular integral equations with a symbol from the Wiener-algebra is given.The approach of dual integral equations has a long history [Mixed Boundary Value Problems in Potential Theory, North-Holland, Amsterdam, 1966] whereas the new developments reviewed in [E. Meister and F. O. Speck, Modern Wiener–Hopf methods in diffraction theory, Proc. Conf. Dundee, 1988, in Ordinary and Partial Differential Equations, B. Sleeman and R. Jarvis, eds., 1989, pp. 130–171] make it possible to handle these equations in Sobolev spaces.
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