On the uniqueness for the Cauchy problem for elliptic equations with triple characteristics (Q1327861)

We prove a uniqueness theorem for the Cauchy problem for a certain elliptic differential operator \(P(x,D)\) in a neighbourhood of the origin in \(\mathbb{R}^ n\) of order \(m \geq 1\) with \(C^ \infty\)-coefficients and the principal symbol \(P_ m (x, \xi)\) of the form \(P_ m (x,\xi)=Q_ 1 (x,\xi)^ 2Q_ 2(x,\xi)\), where \(Q_ i(i=1,2)\) are homogeneous polynomials in \(\xi\) of degree \(m_ i\) with \(C^ \infty\)-coefficients such that if \(m_ i \geq 1\), for every \(\xi' \in \mathbb{R}^{n-1} \backslash \{0\}\) the zeros \(\tau\) of \(Q_ i (0,(\tau,\xi'))\) are non-real and simple.