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Variational properties of a generic model equation in exterior 3D domains. (English) Zbl 1114.35053
Summary: We study a generic model equation in an exterior domain. We assume the case of a non-constant coefficient function. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces. As the main tool we derive and apply an inequality of the Friedrichs-Poincaré type.

35J20 Variational methods for second-order elliptic equations
76M30 Variational methods applied to problems in fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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