SPECTRAL GAPS IN THE DIRICHLET AND NEUMANN PROBLEMS ON THE PLANE PERFORATED BY A DOUBLE- PERIODIC FAMILY OF CIRCULAR HOLES

S. A. Nazarov; K. Ruotsalainen; J. Taskinen

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SPECTRAL GAPS IN THE DIRICHLET AND NEUMANN PROBLEMS ON THE PLANE PERFORATED BY A DOUBLE- PERIODIC FAMILY OF CIRCULAR HOLES

机译：圆孔双周期家族在平面上的狄利克雷和努曼问题的谱隙

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We show that the spectrum of the Dirichlet and Neumann problems for the Laplace operator in the plane perforated by a double-periodic family of circular holes contains gaps (even any a priori given number of gaps) of certain radii of holes. The result is obtained by asymptotic analysis of the cell spectral problem, interpreted as a problem in a domain with thin bridges. Some open questions are stated. Bibliography: 48 titles. Illustrations: 12 figures.

机译：我们表明，在由双周期圆孔家族穿孔的平面中，拉普拉斯算子的Dirichlet和Neumann问题的谱包含某些孔半径的间隙（甚至是任何给定数量的间隙）。通过对细胞光谱问题的渐进分析获得结果，该问题被解释为具有薄桥的区域中的问题。提出了一些未解决的问题。参考书目：48种。插图：12位数字。

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《Journal of Mathematical Sciences》 |2012年第2期|p.164-222|共59页
作者
S. A. Nazarov; K. Ruotsalainen; J. Taskinen;
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Institute for Problems in Mechanical Engineering RAS 61, Bolshoi pr. V.O., St. Petersburg 199178, Russia;

University of Oulu P.O. Box 4500, 90014, Oulu, Finland;

University of Helsinki P.O.Box 68 FIN-00014 Helsinki Finland;

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2. Gaps in the spectrum of the neumann problem on a perforated plane [J] . Nazarov S.A., Ruotsalainen K., Taskinen J. Doklady. Mathematics . 2012,第1期

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SPECTRAL GAPS IN THE DIRICHLET AND NEUMANN PROBLEMS ON THE PLANE PERFORATED BY A DOUBLE- PERIODIC FAMILY OF CIRCULAR HOLES

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