In this talk, we discuss the self-adjointness in -setting of the operators acting as , with piecewise constant functions having a jump along a Lipschitz hypersurface , without explicit assumptions on the sign of . We establish a number of sufficient conditions for the selfadjointness of the operator with -regularity in terms of the jump value and the regularity and geometric properties of . An important intermediate step is a link with Fredholm properties of the NeumannPoincaré operator on , which is new for the Lipschitz setting.
