To spectral problems for the volume potential

被引：51

作者：

Kal'menov, T. Sh. ^{[1
]}

Suragan, D. ^{[1
]}

机构：

[1] Minist Educ & Sci Kazakhstan, Res Ctr Phys & Math, Ul Shevchenko 28, Alma Ata 050010, Kazakhstan

来源：

DOKLADY MATHEMATICS | 2009年 / 80卷 / 02期

关键词：

Eigenvalues and eigenfunctions - Mathematical operators - Poisson equation;

D O I：

10.1134/S1064562409050032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A boundary condition on the volume potential was demonstrated for an arbitrary domain ω. The eigenvalues and the eigen-functions of the volume potential were found for the 2 disk and the 3 ball. It was shown in the Poisson equation that self adjoint differential operators were generated by boundary conditions. One of the main results of the investigation gave boundary conditions uniquely determining the volume potential. The first theorem stated that the spectral problem on the eigenvalues of the volume potential on the disk was equivalent to the spectral problem.

引用

页码：646 / 649

页数：4