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$L_p$-Theory of Boundary Integral Equations on a Contour with Inward Peak

1998
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Zeitschrift für Analysis und ihre Anwendungen
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Boundary integral equations of the second kind in the logarithmic potential theory are studied under the assumption that the contour has an inward peak. For each equation we find a pair of function spaces such that the corresponding operator bijectively maps one of them onto another. and the Neumann problem Au =0 in ci au (1.2) ônr J in a bounded plane simply connected domain ci with inward peak z = 0 on the boundary 1'. Here and elsewhere we assume that the normal n is directed outwards. We

doi:10.4171/zaa/843
fatcat:esrkre75wjal3eebaaaohyrr6q