Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 10, 6 p.

Asymptotics with sharp remainder estimates are recovered for number $\mathbf{N}\left(\tau \right)$ 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 $exp\left(-|x{|}^{m+1}$) width ; $m>0$) and recover eigenvalue asymptotics with sharp remainder estimates.

@article{SEDP_1998-1999____A10_0,
author = {Ivrii, Victor},
title = {Eigenvalue asymptotics for {Neumann} {Laplacian} in domains with ultra-thin cusps},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
note = {talk:10},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {1998-1999},
mrnumber = {1721328},
zbl = {1061.35504},
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url = {http://www.numdam.org/item/SEDP_1998-1999____A10_0/}
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Ivrii, Victor. Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 10, 6 p. http://www.numdam.org/item/SEDP_1998-1999____A10_0/

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