Carleman Parabola and the Eigenvalues of Elliptic Operators

Abstract

We study the problem of location of the spectrum of an elliptic operator in a bounded domain with both the classical and more special boundary conditions. On the complex plane, we construct the set of all eigenvalues of the corresponding operator and consider several examples to illustrate the “asymptotic accuracy” of the obtained set and consider an example of nonunique solvability of a parabolic inverse problem with final observation.