Geodesic
On the dimension of the solution space of elliptic systems in unbounded domains
Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 411-434 
A. A. Kon'kov. On the dimension of the solution space of elliptic systems in unbounded domains. Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 411-434. http://geodesic.mathdoc.fr/item/SM_1995_80_2_a7/
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     title = {On the dimension of the~solution space of elliptic systems in unbounded domains},
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Voir la notice de l'article provenant de la source Math-Net.Ru

This article is a study of the Dirichlet problem $$ \begin{cases} Lu=0&\text{in}\ \Omega, \\ \partial^\alpha u\big|_{\partial \Omega}=0,&|\alpha|\leqslant m-1, \end{cases} $$ where $\Omega\subset R^n$ is an open (possibly unbounded) set, $\alpha=(\alpha_1,\dots,\alpha_n)$ is a multi-index, $|\alpha|=\alpha_1+\dots+\alpha_n$, $$ L=\sum_{|\alpha|=|\beta|=m}\partial^\alpha \bigl(a_{\alpha\beta}(x)\partial^\beta\bigr), $$ and the coefficients $a_{\alpha\beta}(x)$ are $N\times N$ matrices.

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