Nodal sets of thin curved layers
| Autor: | Matěj Tušek, David Krejčiřík |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Mathematics - Differential Geometry
Euclidean space Applied Mathematics Mathematical analysis FOS: Physical sciences Mathematical Physics (math-ph) Mathematics::Spectral Theory Eigenfunction Mathematics - Spectral Theory symbols.namesake Mathematics - Analysis of PDEs Hypersurface Differential Geometry (math.DG) Elliptic partial differential equation Principal curvature FOS: Mathematics symbols Spectral Theory (math.SP) Laplace operator Neighbourhood (mathematics) Mathematical Physics Analysis Schrödinger's cat Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Journal of Differential Equations. 258:281-301 |
| ISSN: | 0022-0396 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect