A Carleman estimate with a weight depending only on y shows that anisotropic exponential/polynomial decay forces u=0 for elliptic inequalities in exterior domains.
Alessandrini, Strong unique continuation for general elliptic eq uations in 2D, J
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Uniqueness of solutions to an elliptic inequality with rapid decay at infinity
A Carleman estimate with a weight depending only on y shows that anisotropic exponential/polynomial decay forces u=0 for elliptic inequalities in exterior domains.