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The Dirichlet problem for Stokes equation in a domain exterior to an open surface

✍ Scribed by V. Kirvalidze


Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
138 KB
Volume
20
Category
Article
ISSN
0170-4214

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✦ Synopsis


The paper deals with the Dirichlet problem for the Stokes linear equation in a domain exterior to an open surface. With the help of the theory of boundary integral (pseudo-differential) equations uniqueness and existence theorems are proved in the Bessel-potential and Besov spaces and C?-smoothness (with ( ) of solution is established in the neighbourhood of the boundary of the open surface.


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The Neumann problem for the Laplace equation in an exterior connected plane region bounded by closed and open curves is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind, which is uniquely solvable.