Quasiconformal mappings and periodic spectral problems in dimension two

Quasiconformal mappings and periodic spectral problems in dimension two
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二维拟共形映射和周期性谱问题

DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
A. Sobolev
A. Sobolev
中科院分区：
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文献类型：
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作者：
E. Shargorodsky;A. Sobolev

文献摘要

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研究了二维二阶周期系数椭圆算子的谱性质。这些运营商的作用在周期性的简单连接波导，无论是狄利克雷，或诺依曼，或第三边界条件。主要的结果是绝对连续的谱，这样的运营商。证明的基石是变量的等温变化，将度量减少到平坦的度量，将波导减少到直条。主要的技术工具是黎曼映射定理的拟共形变体。
We study spectral properties of second-order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition. The main result is the absolute continuity of the spectra of such operators. The cornerstone of the proof is an isothermal change of variables, reducing the metric to a flat one and the waveguide to a straight strip. The main technical tool is the quasiconformal variant of the Riemann mapping theorem.