TRANSMISSION BOUNDARY PROBLEMS FOR DIRACOPERATORS ON LIPSCHITZ DOMAINS AND APPLICATIONSTO MAXWELL'S AND HELMHOLTZ'S EQUATIONS

摘要

The transmission boundary value problem for a perturbed Dirac operator on arbitrary bounded Lipschitz domains in 1R3 is formulated and solved in terms of layer potentials of Clifford-Cauchy type. As a byproduct of t his analysis, an elliptization procedure for the Maxwell system is devised which allows us to show that the Maxwell and Helmholtz transmission bound-ary value problems are well-posed as a corollary of the unique solvability of this more general Dirac transmission problem.