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We prove a general integration by parts formula for first-order differential operators on submanifolds of arbitrary codimension of a given Riemannian manifold. The differential operators in question are assumed to satisfy a suitable tangentiality condition. Several particular cases, particularly relevant to applications to PDE arising in mathematical physics are discussed. Copyright © 2004 John Wiley & Sons, Ltd.

We study the well-posedness of the half-Dirichlet and Poisson problems for Dirac operators in three-dimensional Lipschitz domains, with a special emphasis on optimal Lebesgue and Sobolev-Besov estimates. As an application, an elliptization procedure for the Maxwell system is devised. Copyright © 2002 John Wiley & Sons, Ltd.

We present a simple, Clifford algebra-based approach to several key results in the theory of Maxwell's equations in non-smooth subdomains of R m . Among other things, we give new proofs to the boundary energy estimates of Rellich type for Maxwell's equations in Lipschitz domains from [20, 10], discuss radiation conditions and the case of variable wave number.