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The Sharp Measure Upper Bound of the Nodal Sets of Neumann Laplace Eigenfunctions on C1,1 Domains (2412.16911v1)
Published 22 Dec 2024 in math.AP
Abstract: Let {\Omega} be a bounded domain in Rn 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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