Combined boundary integral equations are used when the classical boundary integral formulation is not unique solvable while the underlying boundary value problem has a unique solution. Well known examples are the Brakhage-Werner or Burton-Miller formulations for exterior Helmholtz problems, or the combined boundary field integral equation approach for the Maxwell system. The unique solvability of combined boundary integral equations strongly relies on the used functional setting. When considering combined boundary integral equations in the natural energy spaces certain regularisations are needed.
In this talk we will describe several regularized combined boundary integral equations for exterior Helmholtz problems and we will discuss possible extensions for the Maxwell system.