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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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##### References:
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