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Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. (English) Zbl 0702.35208
The paper deals with the boundary value problem div U\(=f\) in \(\Omega \subset R^ 2\), \(U=g\) on \(\partial \Omega\), if \(\int_{\Omega}f=\int_{\partial \Omega}g\cdot \nu\) what is the necessary condition for the existence of a solution U. If \(\partial \Omega\) is smooth, then a simple construction of U is possible. This construction fails in the case of non-smooth \(\partial \Omega\). The main result of the paper is the existence of the bounded linear map which is the inverse operator with respect to the above Dirichlet boundary value problem on a polygonal domain \(\Omega\).
Reviewer: I.Bock

MSC:
35Q35 PDEs in connection with fluid mechanics
35J99 Elliptic equations and elliptic systems
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