On the uniqueness of solution to the Cauchy problem for elliptic equations in two variables (Q1176252)

In this paper the author gives a positive result for the uniqueness of the Cauchy problem in case of elliptic equations with smooth coefficients of two independent variables and with triple characteristics. The main result is the following: Theorem. Let \(P\) be a linear elliptic operator of order \(m\) \((m\geq 1)\) with \(C^ \infty\) coefficients in an open neighbourhood \(\omega\) of the origin in \(\mathbb{R}^ 2\). Under certain assumptions on the principal symbol one can find an open neighbourhood \(\omega'\subset\omega\) of the origin such that every \(u\in C^ \infty(\omega)\) satisfying \(Pu= 0\) and \(u|_{t\leq 0}=0\) vanishes in \(\omega'\). The idea of proof is a factorization of the symbol of the operator modulo terms of order less than its order minus one.