  Eigenvalues arising in scattering theory have been envisioned as a potential
source of target signatures in nondestructive testing of materials, whereby
perturbations of the eigenvalues computed for a penetrable medium would be used
to infer changes in its constitutive parameters relative to some reference
values. We consider a recently introduced modification of the class of Stekloff
eigenvalues, in which the inclusion of a smoothing operator guarantees that
infinitely many eigenvalues exist under minimal assumptions on the medium, and
we derive precise formulas that quantify the perturbation of a simple
eigenvalue in terms of the coefficients of a perturbed inhomogeneous medium.
These formulas rely on the theory of nonlinear eigenvalue approximation and
regularity results for elliptic boundary-value problems with heterogeneous
coefficients, the latter of which is shown to have a strong influence on the
sensitivity of the eigenvalues corresponding to an anisotropic medium. A simple
numerical example in two dimensions is used to verify the estimates and suggest
future directions of study.

Analysis of PDEs