First Order Approach to $L^p$ L p Estimates for the Stokes Operator on Lipschitz Domains - Archive ouverte HAL Access content directly
Conference Papers Year : 2016

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

Alan Mcintosh
• Function : Author
• PersonId : 1002489
Sylvie Monniaux

#### Abstract

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

#### Domains

Mathematics [math] Analysis of PDEs [math.AP]

### Dates and versions

hal-01474843 , version 1 (23-02-2017)

### Identifiers

• HAL Id : hal-01474843 , version 1
• DOI :

### Cite

Alan Mcintosh, Sylvie Monniaux. First Order Approach to $L^p$ L p Estimates for the Stokes Operator on Lipschitz Domains. 10th International International Society for Analysis, its Applications and Computation Congress (ISAAC 2015), Aug 2015, Macao, China. pp.55 - 75, ⟨10.1007/978-3-319-41945-9_3⟩. ⟨hal-01474843⟩

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