Eigenvalue Asymptotics for Weighted Polyharmonic Operator with a Singular Measure in the Critical Case

G. V. Rozenblum; E. M. Shargorodsky

doi:10.1134/S001626632102009X

Eigenvalue Asymptotics for Weighted Polyharmonic Operator with a Singular Measure in the Critical Case

G. V. Rozenblum^*, E. M. Shargorodsky

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Abstract: We find that, in the critical case (Formula presented.), the eigenvalues of the problem (Formula presented.) with the singular measure P supported on a compact Lipschitz surface of an arbitrary dimension in (Formula presented.) satisfy an asymptotic formula of the same order as in the case of an absolutely continuous measure.

Original language	English
Pages (from-to)	170-173
Number of pages	4
Journal	Functional Analysis and its Applications
Volume	55
Issue number	2
DOIs	https://doi.org/10.1134/S001626632102009X
Publication status	Published - Apr 2021

Keywords

eigenvalues
singular measures

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10.1134/S001626632102009X

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title = "Eigenvalue Asymptotics for Weighted Polyharmonic Operator with a Singular Measure in the Critical Case",

abstract = "Abstract: We find that, in the critical case (Formula presented.), the eigenvalues of the problem (Formula presented.) with the singular measure P supported on a compact Lipschitz surface of an arbitrary dimension in (Formula presented.) satisfy an asymptotic formula of the same order as in the case of an absolutely continuous measure.",

keywords = "eigenvalues, singular measures",

author = "Rozenblum, {G. V.} and Shargorodsky, {E. M.}",

note = "Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = apr,

doi = "10.1134/S001626632102009X",

language = "English",

volume = "55",

pages = "170--173",

journal = "Functional Analysis and its Applications",

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TY - JOUR

T1 - Eigenvalue Asymptotics for Weighted Polyharmonic Operator with a Singular Measure in the Critical Case

AU - Rozenblum, G. V.

AU - Shargorodsky, E. M.

PY - 2021/4

Y1 - 2021/4

N2 - Abstract: We find that, in the critical case (Formula presented.), the eigenvalues of the problem (Formula presented.) with the singular measure P supported on a compact Lipschitz surface of an arbitrary dimension in (Formula presented.) satisfy an asymptotic formula of the same order as in the case of an absolutely continuous measure.

AB - Abstract: We find that, in the critical case (Formula presented.), the eigenvalues of the problem (Formula presented.) with the singular measure P supported on a compact Lipschitz surface of an arbitrary dimension in (Formula presented.) satisfy an asymptotic formula of the same order as in the case of an absolutely continuous measure.

KW - eigenvalues

KW - singular measures

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U2 - 10.1134/S001626632102009X

DO - 10.1134/S001626632102009X

M3 - Article

AN - SCOPUS:85118710537

SN - 0016-2663

VL - 55

SP - 170

EP - 173

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

IS - 2

ER -

Eigenvalue Asymptotics for Weighted Polyharmonic Operator with a Singular Measure in the Critical Case

Abstract

Keywords

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