Square integrable surface potentials on non-smooth domains and application to the Laplace equation in L2

Motivated by applications in fluid dynamics involving the harmonic Bergman projection, we aim to extend the theory of single and double layer potentials (well documented for functions with H ℓoc 1 regularity) to locally square integrable functions. Having in mind numerical simulations for which functions are usually defined on a polygonal mesh, we wish this theory to cover the cases of non-smooth domains (i.e.with Lipschitz continuous or polygonal boundaries).