Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds

Hofmann, Steve; Mitrea, Marius; Monniaux, Sylvie

doi:10.5802/aif.2642

Cited by 5 publications

(5 citation statements)

References 18 publications

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“…To our knowledge, the fact that they have a functional calculus is new, due to [14]. It was proved in [10] that for the same range of p the Riesz transforms…”

Section: P Results For D H ∆ H and S H P H < P < P Hmentioning

confidence: 99%

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

McIntosh

Monniaux

2016

Springer Proceedings in Mathematics &Amp; Statistics

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International audienceThis 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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“…To our knowledge, the fact that they have a functional calculus is new, due to [14]. It was proved in [10] that for the same range of p the Riesz transforms…”

Section: P Results For D H ∆ H and S H P H < P < P Hmentioning

confidence: 99%

“…We remark that such an iteration method has been used previously in [9] in the study of more general first order systems on R n . A similar iteration procedure has been used also in [17] and [10].…”

Section: Remarks On Obtaining Resolvent Bounds In the Hodge Rangementioning

confidence: 99%

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

McIntosh

Monniaux

2016

Springer Proceedings in Mathematics &Amp; Statistics

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“…These results have been subsequently extended into various directions. As a sample of the extensive literature on this topic, we mention [15,[44][45][46]56] (for the Witten Laplacian); see also [3,4,10,19,37,42,47,49,52,54] (for the Laplace-Beltrami operator), [17,31,51] (for the Hodge-de Rham Laplacian), and [11] (for sub-elliptic operators).…”

Section: Introductionmentioning

confidence: 99%

$$L^p$$-Analysis of the Hodge–Dirac Operator Associated with Witten Laplacians on Complete Riemannian Manifolds

Neerven

Versendaal

2017

J Geom Anal

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“…These results have been subsequently extended into various directions. As a sample of the extensive literature on this topic we mention [15,44,45,46,56] (for the Witten Laplacian); see also [3,4,10,19,37,42,47,49,52,54] (for the Laplace-Beltrami operator), [17,31,51] (for the Hodge-de Rham Laplacian), and [11] (for sub-elliptic operators).…”

Section: Introductionmentioning

confidence: 99%

$L^p$-Analysis of the Hodge--Dirac operator associated with Witten Laplacians on complete Riemannian manifolds

Neerven¹,

Versendaal²

2017

Preprint

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Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds

Cited by 5 publications

References 18 publications

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

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

$$L^p$$-Analysis of the Hodge–Dirac Operator Associated with Witten Laplacians on Complete Riemannian Manifolds

$L^p$-Analysis of the Hodge--Dirac operator associated with Witten Laplacians on complete Riemannian manifolds

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