Mathematical Physics

    

On the Nodal Lines of Eigenfunctions of Laplacian in Plane

Authors: Soo Sun Ha

We prove Payne's nodal line conjecture for any bounded simply connected, possibly non-convex, smooth boundary domain $Omega$ in Plane: Payne conjectured that any Dirichlet second eigenfunction of laplacian in any simply connected boundary domain in Plane can not have a closed nodal line.

Comments: 55 Pages.

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Submission history

[v1] 2023-12-09 22:44:44
[v2] 2024-01-07 21:19:58
[v3] 2024-11-09 02:34:33

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