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Motivated by applications in fluid dynamics involving the harmonic Bergmanprojection we aim at extending the theory of single and double layer potentials(well documented for functions with $H^1_{\ell oc}$ regularity) to locallysquare integrable functions. Having in mind numerical simulations in whichfunctions are usually defined on a polygonal mesh, we wish this theory to coverthe cases of non-smooth domains (i.e.with Lipschitz continuous or polygonalboundaries).

Square integrable surface potentials on non-smooth domains and application to the Laplace equation in $L^2$