Comparison of the singular numbers of correct restrictions of elliptic differential operators

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 Rn with sufficiently smooth boundary, which is in general a nonselfadjoint operator. Conditions are established on a correct restriction, ensuring that its singular numbers sk are of order k 2l/n as k → ∞. As an application of this result certain estimates are obtained for the deviation upon domain perturbation of singular numbers of such correct restrictions. §