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

Ivrii, Victor

Ivrii, Victor ¹

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

Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 10, 6 p.

Résumé

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.

MR Zbl

Affiliations des auteurs :

Ivrii, Victor ¹

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

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     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},
     pages = {1--6},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {1998-1999},
     zbl = {1061.35504},
     mrnumber = {1721328},
     language = {fr},
     url = {https://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. https://www.numdam.org/item/SEDP_1998-1999____A10_0/

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