On eigenvalue asymptotics for strong delta-interactions supported by surfaces with boundaries

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F16%3A00458924" target="_blank" >RIV/61389005:_____/16:00458924 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/16:00307465
Result on the web
<a href="http://dx.doi.org/10.3233/ASY-151341" target="_blank" >http://dx.doi.org/10.3233/ASY-151341</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3233/ASY-151341" target="_blank" >10.3233/ASY-151341</a>

Result language
angličtina
Original language name
On eigenvalue asymptotics for strong delta-interactions supported by surfaces with boundaries
Original language description
Let S subset of R-3 be a C-4-smooth relatively compact orientable surface with a sufficiently regular boundary. For beta is an element of R+, let E-j(beta) denote the jth negative eigenvalue of the operator associated with the quadratic form nH-1(R-3) (sic) u (sic) integral integral integral(R3) vertical bar del u vertical bar(2) dx - beta integral integral(s) vertical bar u vertical bar(2) d sigma where sigma is the two-dimensional Hausdorff measure on S. We show that for each fixed j one has the asymptotic expansion E-j(beta) = -beta(2)/4 + mu(D)(j) + o(1) as beta -> +infinity where mu(D)(j) is the jth eigenvalue of the operator -Delta s +K - M-2 on L-2 (S), in which K and M are the Gauss and mean curvatures, respectively, and As is the Laplace Beltrami operator with the Dirichlet condition at the boundary of S. If, in addition, the boundary of S is C-2-smooth, then the remainder estimate can be improved to O(beta(-1) log beta).
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
BE - Theoretical physics
OECD FORD branch
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Project
<a href="/en/project/GA14-06818S" target="_blank" >GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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