Nodal sets of thin curved layers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F15%3A00442889" target="_blank" >RIV/61389005:_____/15:00442889 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/15:00227993
Result on the web
<a href="http://dx.doi.org/10.1016/j.jde.2014.09.009" target="_blank" >http://dx.doi.org/10.1016/j.jde.2014.09.009</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2014.09.009" target="_blank" >10.1016/j.jde.2014.09.009</a>

Result language
angličtina
Original language name
Nodal sets of thin curved layers
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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