Approximation of eigenvalues of elliptic operators with discontinuous coefficients

Jimbo S.; Kosugi S.

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Approximation of eigenvalues of elliptic operators with discontinuous coefficients

机译：具有不连续系数的椭圆算子特征值的逼近

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The asymptotic behavior of eigenvalues of an elliptic operator with a divergence form is discussed. The coefficients of the operator are discontinuous through a boundary of a subdomain and degenerate to zero on the subdomain when a parameter tends to zero. We will prove that the eigenvalues approach eigenvalues of the Laplacian on the subdomain or on the complement. We will obtain precise asymptotic behavior of their convergence. [References: 13]

机译：讨论了具有散度形式的椭圆算子特征值的渐近行为。运算符的系数在子域的边界处不连续，并且当参数趋于零时在子域上退化为零。我们将证明特征值在子域或补码上接近拉普拉斯算子的特征值。我们将获得它们收敛的精确渐近行为。 [参考：13]

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《Communications in Partial Differential Equations》 |2003年第8期|共21页
作者
Jimbo S.; Kosugi S.;
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正文语种 eng
中图分类偏微分方程;
关键词
Asymptotic expansion; Eigenvalue; Elliptic operator; Singularly perturbed domain; Manifolds; Holes;

机译：渐近展开特征值椭圆算子奇摄动域流形孔;

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专利

1. Approximation of eigenvalues of elliptic operators with discontinuous coefficients [J] . Jimbo S., Kosugi S. Communications in Partial Differential Equations . 2003,第7a8期

机译：具有不连续系数的椭圆算子特征值的逼近
2. On Resolvent Approximations of Elliptic Differential Operators with Locally Periodic Coefficients [J] . Lobachevskii journal of mathematics . 2020,第5期

机译：关于局部周期系数的椭圆微分算子的解析近似
3. Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with control in matching boundary conditions [J] . Lubyshev F. V., Manapova A. R., Fairuzov M. E. Computational mathematics and mathematical physics . 2014,第11期

机译：具有不连续系数和解且具有匹配边界条件下的控制的半线性椭圆型方程的最优控制问题的逼近
4. Maximal L_p-Regularity for Second Order Elliptic Operators with Uniformly Continuous Coefficients on Domains [C] . Peer C. Kunstmann International conference on evolution equation . 2003

机译：用于二阶椭圆算子的最大L_P定期具有均匀连续系数的域
5. Numerical construction of Green's functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations. [D] . Biagioni, David Joseph. 2012

机译：具有变系数的高维椭圆问题中格林函数的数值构造，以及通过稀疏和可分离近似分析可再生能源数据。
6. Adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients [O] . Kelin Xia, Meng Zhan, Decheng Wan, -1

机译：具有不连续系数的椭圆方程的自适应变形网状界面方法
7. On Resolvent Approximations of Elliptic Differential Operators with Locally Periodic Coefficients [O] . S. E. Pastukhova 2020

机译：关于局部周期系数的椭圆微分算子的解析逼近
8. Multilevel Preconditioners for Discontinuous Galerkin Approximations of Elliptic Problems with Jump Coefficients. [R] . B. A. De Dios L. Zikatanov M. Holst Y. Zhu 2010

机译：具有跳跃系数的椭圆问题的间断Galerkin逼近的多级预处理器。

Approximation of eigenvalues of elliptic operators with discontinuous coefficients

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