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