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# The Dirichlet to Neumann map - An application to the Stokes problem in half space

• We illustrate the use of the Dirichlet to Neumann map for elliptic and parabolic problems in the context of the Stokes problems. An analogous representation to that obtained by Solonnikov in [5] for the case of a sphere is given for the half space problem. The validity of this representation is obtained establishing properties of the $\DtN$ map for the Laplace and Heat operators.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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