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Duality in the spaces of solutions of elliptic systems. (English) Zbl 0919.35040
The aim of this paper is to investigate the structure of the strong dual of the space of solutions of a linear elliptic system $$Pu= 0$$ on an open subset of $$\mathbb{R}^N$$ (both determined and overdetermined elliptic systems are considered).
The main result proved in the paper is the following: Let $$X$$ be an open set in $$\mathbb{R}^N$$ and let the coefficients in $$P$$ be real analytic on $$X$$. Assume that $$D\subset\subset X$$ is a domain with real analytic boundary and that $$U^*\subset U$$ are neighbourhoods of the closure of $$D$$. Then the space of solutions of $$Pu= 0$$ on the closure of $$D$$ is topologically equivalent to the dual of the space of solutions of $$Pu= 0$$ on $$D$$.

##### MSC:
 35J45 Systems of elliptic equations, general (MSC2000) 35A20 Analyticity in context of PDEs
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##### References:
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