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This article is cited in 19 scientific papers (total in 19 papers)
Research Papers
Homogenization of periodic differential operators of high order
N. A. Veniaminov St. Petersburg State University, Faculty of Physics, St. Petersburg, Russia
Abstract:
A periodic differential operator of the form $A_\varepsilon=(\mathbf D^p)^*g(\mathbf x/\varepsilon)\mathbf D^p$ is considered on $L_2(\mathbb R^d)$; here $g(x)$ is a positive definite symmetric tensor of order $2p$ periodic with respect to a lattice $\Gamma$. The behavior of the resolvent of the operator $A_\varepsilon$ as $\varepsilon\to0$ is studied. It is shown that the resolvent $(A_\varepsilon+I)^{-1}$ converges in the operator norm to the resolvent of the effective operator $A^0$ with constant coefficients. For the norm of the difference of resolvents, an estimate of order $\varepsilon$ is obtained.
Keywords:
periodic differential operators, averaging, homogenization, threshold effect, operators of high order.
Received: 28.01.2010
Citation:
N. A. Veniaminov, “Homogenization of periodic differential operators of high order”, Algebra i Analiz, 22:5 (2010), 69–103; St. Petersburg Math. J., 22:5 (2011), 751–775
Linking options:
https://www.mathnet.ru/eng/aa1205 https://www.mathnet.ru/eng/aa/v22/i5/p69
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Abstract page: | 558 | Full-text PDF : | 199 | References: | 80 | First page: | 11 |
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