Geodesic
A~strong zero theorem for an elliptic equation of high order
Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 349-367

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In this article we examine a uniformly elliptic equation of high order with simple complex characteristics and with coefficients from $C^1$, defined in a domain $\Omega\subset R^n$ and satisfying there a supplementary condition. At the point $x_0\in\Omega$ let the solution $u(x)$ of this equation have a zero of infinite order. It is shown that then $u\equiv0$ in $\Omega$. Whence a uniqueness theorem is derived for the solution of the Cauchy problem for the equation in question, when the Cauchy data are prescribed on an $(n-1)$-dimensional set of positive measure in the interior of the domain. Bibliography: 10 titles. 
@article{SM_1970_10_3_a4,
     author = {E. G. Sitnikova},
     title = {A~strong zero theorem for an elliptic equation of high order},
     journal = {Sbornik. Mathematics},
     pages = {349--367},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_10_3_a4/}
}
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E. G. Sitnikova. A~strong zero theorem for an elliptic equation of high order. Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 349-367. http://geodesic.mathdoc.fr/item/SM_1970_10_3_a4/