Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains
Annales de l'I.H.P. Analyse non linéaire (2009)
- Volume: 26, Issue: 2, page 547-560
- ISSN: 0294-1449
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topBorisov, Denis, and Freitas, Pedro. "Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains." Annales de l'I.H.P. Analyse non linéaire 26.2 (2009): 547-560. <http://eudml.org/doc/78855>.
@article{Borisov2009,
author = {Borisov, Denis, Freitas, Pedro},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {spectrum; eigenvalue asymptotics; thin domains; Laplace operator; Dirichlet boundary conditions},
language = {eng},
number = {2},
pages = {547-560},
publisher = {Elsevier},
title = {Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains},
url = {http://eudml.org/doc/78855},
volume = {26},
year = {2009},
}
TY - JOUR
AU - Borisov, Denis
AU - Freitas, Pedro
TI - Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 2
SP - 547
EP - 560
LA - eng
KW - spectrum; eigenvalue asymptotics; thin domains; Laplace operator; Dirichlet boundary conditions
UR - http://eudml.org/doc/78855
ER -
References
top- [1] Antunes P., Freitas P., A numerical study of the spectral gap, J. Phys. A41 (2008). Zbl1142.35054MR2433425
- [2] Berezin F.A., Shubin M.A., The Schrödinger Equation, Kluwer, Dordrecht, 1991. Zbl0749.35001MR1186643
- [3] Freitas P., Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi, J. Funct. Anal.251 (2007) 376-398. Zbl1137.35049MR2353712
- [4] P. Freitas, D. Krejčiřík, A sharp upper bound for the first Dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains, Proc. Amer. Math. Soc., in press. Zbl1147.58030MR2399068
- [5] L. Friedlander, M. Solomyak, On the spectrum of the Dirichlet Laplacian in a narrow strip, preprint, 2007. Zbl1173.35090MR2506330
- [6] Joseph D.D., Parameter and domain dependence of eigenvalues of elliptic partial differential equations, Arch. Ration. Mech. Anal.24 (1967) 325-351. Zbl0152.11302MR208194
- [7] Ladyzhenskaya O.A., Uraltseva N.N., Linear and Quasilinear Elliptic Equations, Academic Press, New York–London, 1968. Zbl0164.13002MR244627
- [8] Olejnik O.A., Shamaev A.S., Yosifyan G.A., Mathematical Problems in Elasticity and Homogenization, Studies in Mathematics and its Applications, vol. 26, North-Holland, Amsterdam, 1992. Zbl0768.73003MR1195131
Citations in EuDML Documents
top- David Krejčiřík, Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions
- Pedro Freitas, Batłomiej Siudeja, Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals
- Denis Borisov, Giuseppe Cardone, Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods
- David Krejčiřík, Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions
- Denis Borisov, Giuseppe Cardone, Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods
- David Krejčiřík, Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions
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