摘要
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 R^2 must intersect the boundary ■Ω at exactly two points.
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 R^2 must intersect the boundary δΩ at exactly two points.
基金
supported by the National Natural Science Foundation of China
the National Basic Research Program of China under Grant No.2011CB808002
the National Research Foundation of South Africa
