锥上狄利克雷问题产生的算子铅笔谱

Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI:10.1070/SM1992V073N01ABEH002533

V. Kozlov, V. Maz'ya

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引用次数: 19

摘要

研究了以特征值决定锥顶点Dirichlet问题解的奇异性的算子铅笔。首先考虑了射线上数据的Dirichlet-Sobolev问题，并描述了相应算子束的特征值和特征函数。然后这个信息被用来表明[2]的结果在某种意义上是最好的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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ON THE SPECTRUM OF THE OPERATOR PENCIL GENERATED BY THE DIRICHLET PROBLEM IN A CONE

The operator pencil whose eigenvalues determine singularities of solutions to the Dirichlet problem at the vertex of a cone is studied. First the Dirichlet-Sobolev problem with data on the ray is considered, and the eigenvalues and eigenfunctions of the corresponding operator pencil are described. Then this information is used to show that the result of [2] is best possible in a sense.

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Mathematics of The Ussr-sbornik

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