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The Robin problem for the scalar Oseen equation. (English) Zbl 1277.31011
Summary: We study the Robin problem for the scalar Oseen equation in an open \(n\)-dimensional set with compact Ljapunov boundary. We prescribe two types of Robin boundary conditions, and prove the unique solvability of these problems as well as a representation formula for the solution in form of a scalar Oseen single layer potential. Moreover, we prove the maximum principle for the solution to the Robin problem of the scalar Oseen equation.
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
35J25 Boundary value problems for second-order elliptic equations
76D07 Stokes and related (Oseen, etc.) flows
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