Mathematical Physics and Harmonic Analysis Seminar

Date: November 17, 2016

Time: 3:00PM - 4:00PM

Location: Bloc 628

Speaker: Julia Meshkova, Chebyshev Laboratory, St.Petersburg State University

Title: Homogenization of elliptic and parabolic Dirichlet problems in a bounded domain

Abstract: Let U⊂ℝ^d be a bounded domain of class C^1,1. In L₂(U; ℂⁿ), we consider a self-adjoint second order elliptic differential operator B_D,ε with the Dirichlet boundary condition. The coefficients of B_D,ε are periodic and depend on x/ε; so, they oscillate rapidly as ε→0. We obtain approximations for the resolvent (B_D,ε-ζ I)^-1 and for the semigroup e^(-B_D,εt), t≥0, both in the L₂→ L₂- and L₂→H¹-norms. The results of such type are called operator error estimates in homogenization theory.

The talk is based on a joint work with T.A. Suslina.