On resolvent approximations of elliptic differential operators with locally periodic coefficients

Svetlana Pastukhova

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arXiv · 2001.02281

On resolvent approximations of elliptic differential operators with locally periodic coefficients

Svetlana Pastukhova

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Abstract

We study the asymptotic behaviour, as the small parameter $\varepsilon$ tends to zero, of the resolvents of uniformly elliptic second-order differential operators with locally periodic coefficients depending on the slow variable $x$ and the fast variable $x/\varepsilon$, with periodicity only in the fast variable. We provide a construction for the leading terms in the operator asymptotics of these resolvents in the sense of $L^2$-operator-norm convergence with order $\varepsilon^2$ remainder estimates. We apply the modified method of the first approximation with the usage of the shift.

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Svetlana Pastukhova. 2020-01-07. On resolvent approximations of elliptic differential operators with locally periodic coefficients. https://arxiv.org/abs/2001.02281

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