University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Operator error estimates for homogenization of elliptic systems with periodic coefficients

Operator error estimates for homogenization of elliptic systems with periodic coefficients

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Periodic and Ergodic Spectral Problems

We study a wide class of matrix elliptic second order differential operators $A_ arepsilon$ in a bounded domain with the Dirichlet or Neumann boundary conditions. The coefficients are assumed to be periodic and depend on $x/ arepsilon$. We are interested in the behavior of the resolvent of $A_ arepsilon$ for small $ arepsilon$. Approximations of this resolvent in the $L_2 o L_2$ and $L_2 o H1$ operator norms are obtained. In particular, a sharp order estimate $$ | (A_ arepsilon – zeta I){-1} – (A0 – zeta I){-1} |_{L_2 o L_2} le C arepsilon $$ is proved. Here $A^0$ is the effective operator with constant coefficients.

This talk is part of the Isaac Newton Institute Seminar Series series.

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