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I am looking for references on eigenfunctions with Neumann boundary condition.

In an article, the author wrote in introduction that when a domain is planar polygon, the second eigenfunctions on it have critical point at vertices. But, I could not find the source. I think this is probably a well-known fact. But I am very interested in the proof.

It may be a famous fact for experts, but I would appreciate it if you could tell me.

I am looking for references on eigenfunctions with Neumann boundary condition.

In an article, the author wrote in introduction that when a domain is planar polygon, the second eigenfunctions on it have critical points at vertices. But, I could not find the source. I think this is probably a well-known fact. But I am very interested in the proof.

It may be a famous fact for experts, but I would appreciate it if you could tell me.