Abstract
We prove the well-posedness of the mixed problem for the Stokes system in a class of Lipschitz domains in ℝn, n ≥ 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 Lamesystem, which has recently been shown to be invertible.
Original language | English |
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Pages (from-to) | 1211-1230 |
Number of pages | 20 |
Journal | Transactions of the American Mathematical Society |
Volume | 362 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2010 |
Keywords
- Layer potentials
- Lipschitz domains
- Mixed boundary value problems
- Stokes system
- Well-posedness
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics