Nodal sets of thin curved layers

0442889 - ÚJF 2016 RIV US eng J - Článek v odborném periodiku
Krejčiřík, David - Tušek, M.
Nodal sets of thin curved layers.
Journal of Differential Equations. Roč. 258, č. 2 (2015), s. 281-301. ISSN 0022-0396. E-ISSN 1090-2732
Grant CEP: GA ČR(CZ) GA14-06818S
Institucionální podpora: RVO:61389005
Klíčová slova: convex domain * wave-guides * asyptotics
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.821, rok: 2015

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.
Trvalý link: http://hdl.handle.net/11104/0245710