On the single layer boundary integral operator for the Dirac equation
Abstract
This paper is devoted to the analysis of the single layer boundary integral operator Cz for the Dirac equation in the two- and three-dimensional situation. The map Cz is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator A0 and z belongs to the resolvent set of A0. In the case of smooth boundaries fine mapping properties and a decomposition of Cz in a 'positive' and 'negative' part are analyzed. The obtained results can be applied in the treatment of Dirac operators with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions that are combined in a critical way.
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