Poisson problems with half-Dirichlet boundary conditions for Dirac operators on nonsmooth manifolds
Dorina Mitrea, Marius Mitrea · 2002
We consider Dirichlet and Poisson type problems for the Maxwell-Dirac operator IDk = d + δ + k dt· on a Lipschitz subdomain Ω of a smooth, Riemannian manifold M. The emphasis is on solutions of finite L energy, i.e. sections u satisfying ∫∫ Ω [|u|2 + |du|2 + |δu|2] dVol < +∞. Our approach relies heavily on the analysis of the spectra of Cauchy type operators naturally associated with the problems at hand.