# American Institute of Mathematical Sciences

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An elementary approach to the 3D Navier-Stokes equations with Navier boundary conditions: Existence and uniqueness of various classes of solutions in the flat boundary case.
June  2010, 3(2): 221-230. doi: 10.3934/dcdss.2010.3.221

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

 1 Department of Mathematics, Oregon State University, Corvallis, OR 97331, United States, United States, United States

Received  April 2009 Published  April 2010

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.
Citation: Ihsane Bikri, Ronald B. Guenther, Enrique A. Thomann. The Dirichlet to Neumann map - An application to the Stokes problem in half space. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 221-230. doi: 10.3934/dcdss.2010.3.221
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