First-kind boundary integral equations for the Dirac operator in 3-dimensional Lipschitz domains

Abstract

We develop novel first-kind boundary integral equations for Euclidean Dirac operators in 3D Lipschitz domains comprising square-integrable potentials and involving only weakly singular kernels. Generalized Gårding inequalities are derived and the boundary integral operators are shown to be Fredholm of index zero. Their finite-dimensional kernels are characterized and their dimension is equal to the sum of the Betti numbers of the domain's boundary.