### Abstract

We study the invertibility of β I + K and β I + K^{′} in L^{2} (∂ 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 R^{n}. Consequently, the spectrum on real line lies in [- frac(1, 2), frac(1, 2)]. Applications to transmission problems are also presented.

Original language | English |
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Pages (from-to) | 179-191 |

Number of pages | 13 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 326 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 Feb 1 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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**Spectral properties of the layer potentials associated with elasticity equations and transmission problems on Lipschitz domains.** / Chang, Tong Keun; Choe, Hi Jun.

Research output: Contribution to journal › Article

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

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

VL - 326

SP - 179

EP - 191

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -