Non-density of nodal lines in the clamped plate problem
Analysis of PDEs
2026-01-01 v2 Spectral Theory
Abstract
We show that, in contrast to the case of Laplace eigenfunctions, the nodal set of high energy eigenfunctions of the clamped plate problem is not necessarily dense, and can in fact exhibit macroscopic "nodal voids". Specifically, we show that there are small deformations of the unit disk admitting a clamped plate eigenfunction of arbitrarily high frequency that does not vanish in a disk of radius 0.44.
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Cite
@article{arxiv.2512.08030,
title = {Non-density of nodal lines in the clamped plate problem},
author = {Alberto Enciso and Josef Greilhuber},
journal= {arXiv preprint arXiv:2512.08030},
year = {2026}
}
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34 pages