First Order Approach to $$L^p$$ L p Estimates for the Stokes Operator on Lipschitz Domains
Résumé
This paper concerns Hodge-Dirac operators DH=d+δ acting in Lp(Ω,Λ) where Ω is a bounded open subset of Rn satisfying some kind of Lipschitz condition, Λ is the exterior algebra of Rn,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 L2(Ω,Λ), d′=δ and DH is self-adjoint, thus having bounded resolvent {(I+itDH)}{t∈R} as well as a bounded functional calculus in L2(Ω,Λ). We investigate the range of values pH
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