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On nodal line of the second eigenfunction of the Laplacian over concave domains in ℝ2

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Abstract

In this note, the Payne’s conjecture from convex domains to concave domains is generalized. It is shown that the nodal line N of the second eigenfunction of the Laplacian over some simply connected concave domain Ω in ℝ2 must intersect the boundary ∂Ω at exactly two points.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Central South University, Changsha, 410075, China

    Dong-Hui Yang

  2. Academy of Mathematics and Systems Science, Academia Sinica, Beijing, 100190, China

    Bao-Zhu Guo

Authors
  1. Dong-Hui Yang
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  2. Bao-Zhu Guo
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Corresponding author

Correspondence to Dong-Hui Yang.

Additional information

This work was supported by the National Natural Science Foundation of China, the National Basic Research Program of China under Grant No. 2011CB808002, and the National Research Foundation of South Africa.

This paper was recommended for publication by Editor FENG Dexing.

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Yang, DH., Guo, BZ. On nodal line of the second eigenfunction of the Laplacian over concave domains in ℝ2 . J Syst Sci Complex 26, 483–488 (2013). https://doi.org/10.1007/s11424-013-1175-9

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  • DOI: https://doi.org/10.1007/s11424-013-1175-9

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