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arXiv · 2412.16911

The Sharp Measure Upper Bound of the Nodal Sets of Neumann Laplace Eigenfunctions on C1,1 Domains

Xiujin Chen·Xiaoping Yang
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Abstract

Let {\Omega} be a bounded domain in R^n with C^{1,1} boundary and let u_{\lambda} be a Neumann Laplace eigenfunction in {\Omega} with eigenvalue {\lambda}. We show that the (n - 1)-dimensional Hausdorff measure of the zero set of u_{\lambda} does not exceed C\sqrt{\lambda}.

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Xiujin Chen, Xiaoping Yang. 2024-12-22. The Sharp Measure Upper Bound of the Nodal Sets of Neumann Laplace Eigenfunctions on C1,1 Domains. https://arxiv.org/abs/2412.16911

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