Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains
We describe the boundary behavior of the nodal lines of eigenfunctions of the fixed membrane problem in convex, possibly nonsmooth, domains. This result is applied to the proof of Payne’s conjecture on the nodal line of second eigenfunctions [P1], by removing theC∞ smoothness assumption which is present in the original proof of Melas [M].
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