Resumen de Hodge–Dirac, Hodge-Laplacian and Hodge–Stokes operators in L p Lp spaces on Lipschitz domains

Alan McIntosh, Sylvie Monniaux

• This paper concerns Hodge–Dirac operators D∥ =d+δ – acting in L p (Ω,Λ) where Ω is a bounded open subset of Rn satisfying some kind of Lipschitz condition, Λ is the exterior algebra of R n d is the exterior derivative acting on the de Rham complex of differential forms on Ω, and δ – is the interior derivative with tangential boundary conditions. In L 2 (Ω,Λ) , δ – =d ∗ and D∥ is self-adjoint, thus having bounded resolvents {(I+itD‖)−1}t∈R as well as a bounded functional calculus in L2(Ω,Λ).