Abstract:
Suppose that $D$ is a bounded domain in $\mathbb R^n(n\geq 2)$ with connected real-analytic boundary, $A$ is an elliptic system with real-analytic coefficients in a neighborhood of the closure $\overline{D}$ of $D$, and ${\rm sol}(A,D)$ is the space of solutions to the system $Au=0$ in $D$ furnished with the standard Frechet–Schwartz topology. Then the dual of ${\rm sol}(A,D)$ epresents the space ${\rm sol}(A,\overline D)$ of solutions to the system $Au=0$ in a neighborhood of $\overline{D}$ furnished with the standard inductive limit topology over some decreasing net of neighborhoods of $\overline{D}$. The corresponding pairing is generated by the inner product in the Lebesgue space $L^2(D)$.
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