Sharp remainder estimates in the Weyl formula for the Neumann Laplacian on a class of planar regions

Y Netrusov

doi:10.1016/j.jfa.2006.11.020

Sharp remainder estimates in the Weyl formula for the Neumann Laplacian on a class of planar regions

Y Netrusov

Research output: Contribution to journal › Article (Academic Journal) › peer-review

10 Citations (Scopus)

Abstract

We obtain estimates for the counting function of the Neumann Laplacian on a planar domain bounded by the graph of a lower semicontinuous L1-function. These estimates imply necessary and sufficient conditions for the validity of the classical one-term Weyl formula for the counting function and, under certain restrictions, give an order sharp remainder estimate in this formula.

Translated title of the contribution	Sharp remainder estimates in the Weyl formula for the Neumann Laplacian on a class of planar regions
Original language	English
Pages (from-to)	21 - 41
Number of pages	21
Journal	Journal of Functional Analysis
Volume	250 (1)
DOIs	https://doi.org/10.1016/j.jfa.2006.11.020
Publication status	Published - Sept 2007

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Publisher: Elsevier Acadmic Press

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title = "Sharp remainder estimates in the Weyl formula for the Neumann Laplacian on a class of planar regions",

abstract = "We obtain estimates for the counting function of the Neumann Laplacian on a planar domain bounded by the graph of a lower semicontinuous L1-function. These estimates imply necessary and sufficient conditions for the validity of the classical one-term Weyl formula for the counting function and, under certain restrictions, give an order sharp remainder estimate in this formula.",

author = "Y Netrusov",

note = "Publisher: Elsevier Acadmic Press",

year = "2007",

month = sep,

doi = "10.1016/j.jfa.2006.11.020",

language = "English",

volume = "250 (1)",

pages = "21 -- 41",

journal = "Journal of Functional Analysis",

issn = "1096-0783",

publisher = "Academic Press Inc.",

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T1 - Sharp remainder estimates in the Weyl formula for the Neumann Laplacian on a class of planar regions

AU - Netrusov, Y

N1 - Publisher: Elsevier Acadmic Press

PY - 2007/9

Y1 - 2007/9

N2 - We obtain estimates for the counting function of the Neumann Laplacian on a planar domain bounded by the graph of a lower semicontinuous L1-function. These estimates imply necessary and sufficient conditions for the validity of the classical one-term Weyl formula for the counting function and, under certain restrictions, give an order sharp remainder estimate in this formula.

AB - We obtain estimates for the counting function of the Neumann Laplacian on a planar domain bounded by the graph of a lower semicontinuous L1-function. These estimates imply necessary and sufficient conditions for the validity of the classical one-term Weyl formula for the counting function and, under certain restrictions, give an order sharp remainder estimate in this formula.

U2 - 10.1016/j.jfa.2006.11.020

DO - 10.1016/j.jfa.2006.11.020

M3 - Article (Academic Journal)

SN - 1096-0783

VL - 250 (1)

SP - 21

EP - 41

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

ER -

Sharp remainder estimates in the Weyl formula for the Neumann Laplacian on a class of planar regions

Abstract

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