Higher regularity in the classical layer potential theory for Lipschitz domains Vladimir Maz'yaTatyana Shaposhnikova 35B6531B1042B2046E35higher regularity of solutionsfractional Sobolev spacesLipschitz domainslayer potentialspointwise multipliers 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 sharp 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. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2668 10.1512/iumj.2005.54.2668 en Indiana Univ. Math. J. 54 (2005) 99 - 142 state-of-the-art mathematics http://iumj.org/access/