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- W4302393026 abstract "This paper is concerned with the location of nodal sets of eigenfunctions of the Dirichlet Laplacian in thin tubular neighbourhoods of hypersurfaces of the Euclidean space of arbitrary dimension. In the limit when the radius of the neighbourhood tends to zero, it is known that spectral properties of the Laplacian are approximated well by an effective Schrodinger operator on the hypersurface with a potential expressed solely in terms of principal curvatures. By applying techniques of elliptic partial differential equations, we strengthen the known perturbation results to get a convergence of eigenfunctions in Holder spaces. This enables us in particular to conclude that every nodal set has a non-empty intersection with the boundary of the tubular neighbourhood." @default.
- W4302393026 created "2022-10-06" @default.
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- W4302393026 date "2014-06-16" @default.
- W4302393026 modified "2023-10-14" @default.
- W4302393026 title "Nodal sets of thin curved layers" @default.
- W4302393026 doi "https://doi.org/10.48550/arxiv.1406.4103" @default.
- W4302393026 hasPublicationYear "2014" @default.
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