ON NODAL LINE OF THE SECOND EIGENFUNCTION OF THE LAPLACIAN OVER CONCAVE DOMAINS IN R2

YANG Dong-Hui , GUO Bao-Zhu

系统科学与复杂性(英文) ›› 2013, Vol. 26 ›› Issue (3) : 483-488.

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系统科学与复杂性(英文) ›› 2013, Vol. 26 ›› Issue (3) : 483-488. DOI: 10.1007/s11424-013-1175-9

ON NODAL LINE OF THE SECOND EIGENFUNCTION OF THE LAPLACIAN OVER CONCAVE DOMAINS IN R2

    YANG Dong-Hui1 , GUO Bao-Zhu2
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ON NODAL LINE OF THE SECOND EIGENFUNCTION OF THE LAPLACIAN OVER CONCAVE DOMAINS IN R2

    YANG Dong-Hui1 , GUO Bao-Zhu2
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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   in R2 must intersect the boundary @  at exactly two points.

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YANG Dong-Hui , GUO Bao-Zhu. ON NODAL LINE OF THE SECOND EIGENFUNCTION OF THE LAPLACIAN OVER CONCAVE DOMAINS IN R2. 系统科学与复杂性(英文), 2013, 26(3): 483-488 https://doi.org/10.1007/s11424-013-1175-9
YANG Dong-Hui , GUO Bao-Zhu. ON NODAL LINE OF THE SECOND EIGENFUNCTION OF THE LAPLACIAN OVER CONCAVE DOMAINS IN R2. Journal of Systems Science and Complexity, 2013, 26(3): 483-488 https://doi.org/10.1007/s11424-013-1175-9
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