Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains

Denis Borisov; Pedro Freitas

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 2, page 547-560
  • ISSN: 0294-1449

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Borisov, 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

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  1. [1] Antunes P., Freitas P., A numerical study of the spectral gap, J. Phys. A41 (2008). Zbl1142.35054MR2433425
  2. [2] Berezin F.A., Shubin M.A., The Schrödinger Equation, Kluwer, Dordrecht, 1991. Zbl0749.35001MR1186643
  3. [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. [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. [5] L. Friedlander, M. Solomyak, On the spectrum of the Dirichlet Laplacian in a narrow strip, preprint, 2007. Zbl1173.35090MR2506330
  6. [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. [7] Ladyzhenskaya O.A., Uraltseva N.N., Linear and Quasilinear Elliptic Equations, Academic Press, New York–London, 1968. Zbl0164.13002MR244627
  8. [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

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  1. Pedro Freitas, Batłomiej Siudeja, Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals
  2. David Krejčiřík, Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions
  3. Denis Borisov, Giuseppe Cardone, Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods
  4. David Krejčiřík, Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions
  5. Denis Borisov, Giuseppe Cardone, Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods
  6. David Krejčiřík, Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions

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