Mathematical Physics and Harmonic Analysis Seminar

Date: April 14, 2023

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Kirill Cherednichenko, University of Bath

Title: Operator-norm homogenisation for Maxwell equations on periodic singular structures

Abstract: I will discuss a new approach to obtaining uniform operator asymptotic estimates in periodic homogenisation. Based on a novel uniform Poincar ́e-type inequality, it bears similarities to the techniques I developed with Cooper (ARMA, 2016) and Velcic (JLMS, 2022).
In the context of the Maxwell system, the analytic framework I will present leads to a new representation for the asymptotics obtained by Birman and Suslina in 2007 for the full system and by Suslina in 2004 for the electric field in the presence of currents. As part of the new asymptotic construction, I will link the leading-order approximation to a family of “homogenised” problems, which was not possible using the earlier method.
The analysis presented applies to a class of inhomogeneous structures modelled by arbitrary periodic Borel measures. However, the results are new even for the particular case of the Lebesgue measure.

This is joint work with Serena D’Onofrio.