Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps

Victor Ivrii[1]

  • [1] Department of Mathematics, University of Toronto, 100, St.George Str., Toronto, Ontario M5S 3G3, CANADA

Séminaire Équations aux dérivées partielles (1998-1999)

  • Volume: 1998-1999, page 1-6

Abstract

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Asymptotics with sharp remainder estimates are recovered for number N ( τ ) of eigenvalues of the generalized Maxwell problem and for related Laplacians which are similar to Neumann Laplacian. We consider domains with ultra-thin cusps (with exp ( - | x | m + 1 ) width ; m > 0 ) and recover eigenvalue asymptotics with sharp remainder estimates.

How to cite

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Ivrii, Victor. "Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps." Séminaire Équations aux dérivées partielles 1998-1999 (1998-1999): 1-6. <http://eudml.org/doc/10960>.

@article{Ivrii1998-1999,
abstract = {Asymptotics with sharp remainder estimates are recovered for number $\{\mathbf\{N\}\}(\tau )$ of eigenvalues of the generalized Maxwell problem and for related Laplacians which are similar to Neumann Laplacian. We consider domains with ultra-thin cusps (with $\exp (-|x| ^\{m+1\}$) width ; $m&gt;0$) and recover eigenvalue asymptotics with sharp remainder estimates.},
affiliation = {Department of Mathematics, University of Toronto, 100, St.George Str., Toronto, Ontario M5S 3G3, CANADA},
author = {Ivrii, Victor},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {domains with cusps; Maxwell operator; Laplacians; eigenvalue asymptotics with sharp remainder estimates},
language = {fre},
pages = {1-6},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps},
url = {http://eudml.org/doc/10960},
volume = {1998-1999},
year = {1998-1999},
}

TY - JOUR
AU - Ivrii, Victor
TI - Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps
JO - Séminaire Équations aux dérivées partielles
PY - 1998-1999
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1998-1999
SP - 1
EP - 6
AB - Asymptotics with sharp remainder estimates are recovered for number ${\mathbf{N}}(\tau )$ of eigenvalues of the generalized Maxwell problem and for related Laplacians which are similar to Neumann Laplacian. We consider domains with ultra-thin cusps (with $\exp (-|x| ^{m+1}$) width ; $m&gt;0$) and recover eigenvalue asymptotics with sharp remainder estimates.
LA - fre
KW - domains with cusps; Maxwell operator; Laplacians; eigenvalue asymptotics with sharp remainder estimates
UR - http://eudml.org/doc/10960
ER -

References

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