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

• Alan G.R. McIntosh ^[1] ; Sylvie Monniaux ^[2]
  1. [1] Australian National University

     Australian National University

     Australia

     
  2. [2] Aix-Marseille University

     Aix-Marseille University

     Arrondissement de Marseille, Francia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 4, 2018, págs. 1711-1753
• Idioma: inglés
• DOI: 10.4171/rmi/1041
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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).