On some estimate of the Carleman type for anisotropic differential operators (Q2719481)

In the domain \(\Omega\subset\mathbb{R}^{n+1}\) the author considers the linear differential operator NEWLINE\[NEWLINE P(x,D) = \sum_{\langle \rho,\alpha\rangle\leq m} a_\alpha(x) D^\alpha,\quad\;D_j = \frac{1}{i} \frac{\partial}{\partial x_j},\tag{1} NEWLINE\]NEWLINE with infinitely differentiable coefficients. The weights \(\rho_j\), \(j=1,2,\dots,n\), are assumed to be positive integers, \(\langle \rho,\alpha\rangle\) denotes the weighted degree of the derivative~\(D^\alpha\) NEWLINE\[NEWLINE \langle \rho,\alpha\rangle = \rho_1\alpha_ 1+\rho_2\alpha_2+\dots+ \rho_n\alpha_n. NEWLINE\]NEWLINE In the paper estimates of Carleman type are given and the corresponding uniqueness theorems for two classes of anisotropic differential operators of type (1) are proved.