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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.
##### MSC:
 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
##### Keywords:
scalar Oseen equation; Oseen potentials; Robin problem
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