A STRONG ZERO THEOREM FOR AN ELLIPTIC EQUATION OF HIGH ORDER
E G Sitnikova · Mathematics of the USSR-Sbornik · 1970
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 Ω ⊂ R n and satisfying there a supplementary condition. At the point x 0 ∊ Ω let the solution u ( x ) of this equation have a zero of infinite order. It is shown that then u ≡0 in Ω . Hence 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 of 10 entries.