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Classical boundary integral equations of the harmonic potential theory on Lipschitz surfaces are studied. We obtain higher fractional Sobolev regularity results for their solutions under weak conditions on the surface. These results are derived from a theorem on the solvability of auxiliary boundary value problems for the Laplace equation in weighted Sobolev spaces. We show that classes of domains under consideration are optimal. 2000 Mathematics Subject Classification: Primary 35B65, 31B10,doi:10.1512/iumj.2005.54.2668 fatcat:s4rgnd237jg4rfaf5g6hftdjhy