First Order Approach to $$L^p$$ Estimates for the Stokes Operator on Lipschitz Domains

This paper concerns Hodge-Dirac operators \(D_H = d + \delta \) acting in \(L^p(\Omega , \Lambda )\) where \(\Omega \) is a bounded open subset of \(\mathbb {R}^n\) satisfying some kind of Lipschitz condition, \(\Lambda \) is the exterior algebra of \(\mathbb {R}^n, d\) is the exterior derivative acting on the de Rham complex of differential forms on \(\Omega \), and \(\delta \) is the interior derivative with tangential boundary conditions. In \(L^2(\Omega , \Lambda )\), \(d' = \delta \) and \(D_H\) is self-adjoint, thus having bounded resolvent \({\{(I + \mathrm{{it}}{D}_H)\}}_{\{t\in \mathbb {R}\}}\) as well as a bounded functional calculus in \(L^2(\Omega , \Lambda )\). We investigate the range of values \(p_H更多