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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the analyticity of the semigroup generated by the Stokes operator with Neumann-type boundary conditions on Lipschitz subdomains of Riemannian manifolds


Authors: Marius Mitrea and Sylvie Monniaux
Journal: Trans. Amer. Math. Soc. 361 (2009), 3125-3157
MSC (2000): Primary 42B30, 46A16; Secondary 46E35, 35J25
Published electronically: December 30, 2008
MathSciNet review: 2485421
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Abstract: We study the analyticity of the semigroup generated by the Stokes operator equipped with Neumann-type boundary conditions on $ L^p$ spaces in Lipschitz domains. Our strategy is to regularize this operator by considering the Hodge Laplacian, which has the additional property that it commutes with the Leray projection.


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Additional Information

Marius Mitrea
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
Email: marius@math.missouri.edu

Sylvie Monniaux
Affiliation: LATP - UMR 6632, Faculté des Sciences de Saint-Jérôme - Case Cour A, Université Aix-Marseille 3, F-13397 Marseille Cédex 20, France
Email: sylvie.monniaux@univ.u-3mrs.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04827-7
PII: S 0002-9947(08)04827-7
Keywords: Hodge-Laplacian, Lipschitz domains, analytic semigroup
Received by editor(s): June 25, 2007
Published electronically: December 30, 2008
Additional Notes: The first author was supported by the NSF grants DMS - 0400639 and DMS FRG - 0456306.
The second author was supported by a UMC Miller Scholarship grant.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.