Unique continuation of boundary over-determined Stokes and Oseeneigenproblems

Roberto Triggiani

doi:10.3934/dcdss.2009.2.645

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2009, Volume 2, Issue 3: 645-677. Doi: 10.3934/dcdss.2009.2.645

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Unique continuation of boundary over-determined Stokes and Oseen eigenproblems

Roberto Triggiani^1,

1.
Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904

Received: September 30, 2008

Revised: November 30, 2008

Published: August 2009

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Abstract

We provide several radically different proofs of the following unique continuation result: The Oseen eigenvalue problem with over-determined homogeneous Cauchy data for the velocity field on the boundary implies the zero solution, at least if the equilibrium solution is sufficiently 'small.' In particular, this unique continuation result from over-determined boundary data holds true for the Stokes problem.

Keywords:

Unique continuation,
Oseen equation.

Mathematics Subject Classification: Primary: 35J70, 47F, 76A, 93C.

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