Improved resolvent 𝐿²-approximations in homogenization of fourth order operators

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2023-07-26 DOI:10.1090/spmj/1772

S. Pastukhova

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引用次数: 2

Abstract

A divergent elliptic operator A ε A_\varepsilon of the fourth order with ε \varepsilon -periodic coefficients acting in the space R d \mathbb {R}^d is treated, where ε \varepsilon is a small parameter. For the resolvent ( A ε + 1 ) − 1 (A_\varepsilon +1)^{-1} , approximations are constructed in the operator ( L 2 → L 2 ) {(L^2\to L^2)} -norm with remainder of order ε 3 \varepsilon ^3 . The method of two-scale expansions with the use of smoothing is employed.

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改进的求解方法𝐿²-四阶算子均匀化的近似

研究了一个具有ε \varepsilon周期系数的四阶发散椭圆算子A ε A_\varepsilon作用于空间rd \mathbb {R}^d，其中ε \varepsilon是一个小参数。对于解(A ε +1)−1 (A_\varepsilon +1)^{-1}，在算子(l2→l2) {(L^2\到L^2)} -范数中构造了近似，余数为ε 3 \varepsilon ^3阶。采用了双尺度展开式平滑法。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.