Andrey L. Piatnitski: First eigenpair asymptotics for singularly perturbed elliptic operators with oscillating coefficients

The talk will focus on Dirichlet spectral problem in a bounded domain for a second order singularly perturbed elliptic operator with locally periodic rapidly oscillating coefficients. Our goal is to describe the limit of the first eigenvalue and the logarithmic asymptotics of the first eigenfunction. Also, in the case of a convection-diffusion operator, we construct the second term of the asymptotics and discuss the non-uniqueness problem.