Abstract
The paper is dedicated to finding the asymptotics of singular numbers of a correct restriction of a uniformly elliptic differential operator of order $2l$ defined on a bounded domain in $\mathbb {R}^n$ with sufficiently smooth boundary, which is in general a non-selfadjoint operator. Conditions are established on a correct restriction, ensuring that its singular numbers $s_k$ are of order $k^{{2l}/n}$ as $k\to \infty$. As an application of this result certain estimates are obtained for the deviation upon domain perturbation of singular numbers of such correct restrictions.