Spectral properties of the layer potentials associated with elasticity equations and transmission problems on Lipschitz domains

Tong Keun Chang; Hi Jun Choe

doi:10.1016/j.jmaa.2006.03.001

Spectral properties of the layer potentials associated with elasticity equations and transmission problems on Lipschitz domains

Tong Keun Chang, Hi Jun Choe

Department of Mathematics

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

4 Citations (Scopus)

Abstract

We study the invertibility of β I + K and β I + K^′ in L² (∂ Ω) for β ∈ R {set minus} [- frac(1, 2), frac(1, 2)] where K, K^′ are double layer potentials related to elasticity equations and Ω is bounded Lipschitz domain in Rⁿ. Consequently, the spectrum on real line lies in [- frac(1, 2), frac(1, 2)]. Applications to transmission problems are also presented.

Original language	English
Pages (from-to)	179-191
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	326
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2006.03.001
Publication status	Published - 2007 Feb 1

Bibliographical note

Funding Information:
This paper is supported by KOSEF R01-2004-000-10072-0. Corresponding author. E-mail addresses: chang7357@yonsei.ac.kr (T.K. Chang), choe@yonsei.ac.kr (H.J. Choe).

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2006.03.001

Cite this

@article{8d3d5bce6fff49b4a236fcbe4ac70aa3,

title = "Spectral properties of the layer potentials associated with elasticity equations and transmission problems on Lipschitz domains",

abstract = "We study the invertibility of β I + K and β I + K′ in L2 (∂ Ω) for β ∈ R {set minus} [- frac(1, 2), frac(1, 2)] where K, K′ are double layer potentials related to elasticity equations and Ω is bounded Lipschitz domain in Rn. Consequently, the spectrum on real line lies in [- frac(1, 2), frac(1, 2)]. Applications to transmission problems are also presented.",

author = "Chang, {Tong Keun} and Choe, {Hi Jun}",

note = "Funding Information: This paper is supported by KOSEF R01-2004-000-10072-0. Corresponding author. E-mail addresses: chang7357@yonsei.ac.kr (T.K. Chang), choe@yonsei.ac.kr (H.J. Choe).",

year = "2007",

month = feb,

day = "1",

doi = "10.1016/j.jmaa.2006.03.001",

language = "English",

volume = "326",

pages = "179--191",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Spectral properties of the layer potentials associated with elasticity equations and transmission problems on Lipschitz domains

AU - Chang, Tong Keun

AU - Choe, Hi Jun

N1 - Funding Information: This paper is supported by KOSEF R01-2004-000-10072-0. Corresponding author. E-mail addresses: chang7357@yonsei.ac.kr (T.K. Chang), choe@yonsei.ac.kr (H.J. Choe).

PY - 2007/2/1

Y1 - 2007/2/1

N2 - We study the invertibility of β I + K and β I + K′ in L2 (∂ Ω) for β ∈ R {set minus} [- frac(1, 2), frac(1, 2)] where K, K′ are double layer potentials related to elasticity equations and Ω is bounded Lipschitz domain in Rn. Consequently, the spectrum on real line lies in [- frac(1, 2), frac(1, 2)]. Applications to transmission problems are also presented.

AB - We study the invertibility of β I + K and β I + K′ in L2 (∂ Ω) for β ∈ R {set minus} [- frac(1, 2), frac(1, 2)] where K, K′ are double layer potentials related to elasticity equations and Ω is bounded Lipschitz domain in Rn. Consequently, the spectrum on real line lies in [- frac(1, 2), frac(1, 2)]. Applications to transmission problems are also presented.

UR - http://www.scopus.com/inward/record.url?scp=33750615835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750615835&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2006.03.001

DO - 10.1016/j.jmaa.2006.03.001

M3 - Article

AN - SCOPUS:33750615835

SN - 0022-247X

VL - 326

SP - 179

EP - 191

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Spectral properties of the layer potentials associated with elasticity equations and transmission problems on Lipschitz domains

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this