skip to content
 

Operator error estimates for homogenization of elliptic systems with periodic coefficients

Presented by: 
T Suslina Saint Petersburg State University
Date: 
Friday 27th March 2015 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
We study a wide class of matrix elliptic second order differential operators $A_\varepsilon$ in a bounded domain with the Dirichlet or Neumann boundary conditions. The coefficients are assumed to be periodic and depend on $x/\varepsilon$. We are interested in the behavior of the resolvent of $A_\varepsilon$ for small $\varepsilon$. Approximations of this resolvent in the $L_2\to L_2$ and $L_2 \to H^1$ operator norms are obtained. In particular, a sharp order estimate $$ \| (A_\varepsilon - \zeta I)^{-1} - (A^0 - \zeta I)^{-1} \|_{L_2 \to L_2} \le C\varepsilon $$ is proved. Here $A^0$ is the effective operator with constant coefficients.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons