Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Asymptotics of Eigenvalues in Spectral Gaps of Periodic Waveguides with Small Singular Perturbations. / Nazarov, S. A.
в: Journal of Mathematical Sciences (United States), Том 243, № 5, 01.12.2019, стр. 746-773.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - Asymptotics of Eigenvalues in Spectral Gaps of Periodic Waveguides with Small Singular Perturbations
AU - Nazarov, S. A.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - The asymptotics of eigenvalues appearing near the lower edge of a spectral gap of the Dirichlet problem is studied for the Laplace operator in a d-dimensional periodic waveguide with a singular perturbation of the boundary by creating a hole with a small diameter ε. Several versions of the structure of the gap edge are considered. As usual, the asymptotic formulas are different in the cases d ≥ 3 and d = 2, where the eigenvalues occur at distances O(ε2(d−2)) or O(ε2d) and O(|ln ε|−2) or O(ε4), respectively, from the gap edge. Other types of singular perturbation of the waveguide surface and other types of boundary conditions are discussed, which provide the appearance of eigenvalues near both edges of one or several gaps.
AB - The asymptotics of eigenvalues appearing near the lower edge of a spectral gap of the Dirichlet problem is studied for the Laplace operator in a d-dimensional periodic waveguide with a singular perturbation of the boundary by creating a hole with a small diameter ε. Several versions of the structure of the gap edge are considered. As usual, the asymptotic formulas are different in the cases d ≥ 3 and d = 2, where the eigenvalues occur at distances O(ε2(d−2)) or O(ε2d) and O(|ln ε|−2) or O(ε4), respectively, from the gap edge. Other types of singular perturbation of the waveguide surface and other types of boundary conditions are discussed, which provide the appearance of eigenvalues near both edges of one or several gaps.
UR - http://www.scopus.com/inward/record.url?scp=85075206544&partnerID=8YFLogxK
U2 - 10.1007/s10958-019-04576-4
DO - 10.1007/s10958-019-04576-4
M3 - Article
AN - SCOPUS:85075206544
VL - 243
SP - 746
EP - 773
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 5
ER -
ID: 60873893