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ISSN 1088-6850(e) ISSN 0002-9947(p)

Mixed boundary value problems for the Stokes system

Author(s): R. Brown; I. Mitrea; M. Mitrea; M. Wright
Journal: Trans. Amer. Math. Soc. 362 (2010), 1211-1230.
MSC (2000): Primary 35J25, 42B20; Secondary 35J05, 45B05, 31B10
Posted: October 9, 2009
MathSciNet review: 2563727
Retrieve article in: PDF

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Abstract: We prove the well-posedness of the mixed problem for the Stokes system in a class of Lipschitz domains in ${\mathbb{R}}^n$ , $n\geq 3$ . The strategy is to reduce the original problem to a boundary integral equation, and we establish certain new Rellich-type estimates which imply that the intervening boundary integral operator is semi-Fredholm. We then prove that its index is zero by performing a homotopic deformation of it onto an operator related to the Lamé system, which has recently been shown to be invertible.

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