Eigenvalue Estimates of Laplacians Defined by Fractal Measures

Sze-Man Ngai

Eigenvalue Estimates of Laplacians Defined by Fractal Measures

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

We study various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined by positive Borel measures on bounded open subsets of Euclidean spaces. These Laplacians and the corresponding eigenvalue estimates differ from classical ones in that the defining measures can be singular. By using properties of self-similar measures, such as Strichartz's second-order self-similar identities, we improve some of the eigenvalue estimates.

Original language	American English
State	Published - Jun 1 2014
Event	Cornell University Conference on Analysis, Probability and Mathematical Physics on Fractals - Duration: Jun 1 2014 → …

Conference

Conference	Cornell University Conference on Analysis, Probability and Mathematical Physics on Fractals
Period	06/1/14 → …

Keywords

Borel probability measure
Dirichlet Laplacian
Eigenfunctions
Eigenvalues
Poincare type inequality

DC Disciplines

Mathematics
Physical Sciences and Mathematics

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Eigenvalue Estimates of Laplacians Defined by Fractal MeasuresFinal published version, 469 KBLicense: Unspecified

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title = "Eigenvalue Estimates of Laplacians Defined by Fractal Measures",

abstract = " We study various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined by positive Borel measures on bounded open subsets of Euclidean spaces. These Laplacians and the corresponding eigenvalue estimates differ from classical ones in that the defining measures can be singular. By using properties of self-similar measures, such as Strichartz's second-order self-similar identities, we improve some of the eigenvalue estimates.",

keywords = "Borel probability measure, Dirichlet Laplacian, Eigenfunctions, Eigenvalues, Poincare type inequality",

author = "Sze-Man Ngai",

year = "2014",

month = jun,

day = "1",

language = "American English",

note = "Cornell University Conference on Analysis, Probability and Mathematical Physics on Fractals ; Conference date: 01-06-2014",

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TY - CONF

T1 - Eigenvalue Estimates of Laplacians Defined by Fractal Measures

AU - Ngai, Sze-Man

PY - 2014/6/1

Y1 - 2014/6/1

N2 - We study various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined by positive Borel measures on bounded open subsets of Euclidean spaces. These Laplacians and the corresponding eigenvalue estimates differ from classical ones in that the defining measures can be singular. By using properties of self-similar measures, such as Strichartz's second-order self-similar identities, we improve some of the eigenvalue estimates.

AB - We study various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined by positive Borel measures on bounded open subsets of Euclidean spaces. These Laplacians and the corresponding eigenvalue estimates differ from classical ones in that the defining measures can be singular. By using properties of self-similar measures, such as Strichartz's second-order self-similar identities, we improve some of the eigenvalue estimates.

KW - Borel probability measure

KW - Dirichlet Laplacian

KW - Eigenfunctions

KW - Eigenvalues

KW - Poincare type inequality

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpres/5

M3 - Presentation

T2 - Cornell University Conference on Analysis, Probability and Mathematical Physics on Fractals

Y2 - 1 June 2014

ER -

Eigenvalue Estimates of Laplacians Defined by Fractal Measures

Abstract

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