Abstract
Let Ω be a bounded domain inRnwithC2-boundary and letDbe a Lipschitz domain withD⊂Ω. We consider the inverse problem (determiningD) to the system of linear elasticityDi((μD(δijδrs+δirδjs)+λDδirδjs)Djus)=0in Ω,where μD=μχD+μχRn\Dand λD=λχD+λχRn\D. Under the condition on the Lamè constants (λ-λ)(μ-μ)≥0, we show thatDis uniquely determined by the complete knowledge of the Dirichlet-to-Neumann map. We also obtain an uniqueness result for the monotone case from one boundary measurement.
| Original language | English |
|---|---|
| Pages (from-to) | 514-531 |
| Number of pages | 18 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 215 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1997 Nov 15 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
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Identification problems in linear elasticity. / Kim, Hyunseok; Seo, Jin Keun.
In: Journal of Mathematical Analysis and Applications, Vol. 215, No. 2, 15.11.1997, p. 514-531.Research output: Contribution to journal › Article
TY - JOUR
T1 - Identification problems in linear elasticity
AU - Kim, Hyunseok
AU - Seo, Jin Keun
PY - 1997/11/15
Y1 - 1997/11/15
N2 - Let Ω be a bounded domain inRnwithC2-boundary and letDbe a Lipschitz domain withD⊂Ω. We consider the inverse problem (determiningD) to the system of linear elasticityDi((μD(δijδrs+δirδjs)+λDδirδjs)Djus)=0in Ω,where μD=μχD+μχRn\Dand λD=λχD+λχRn\D. Under the condition on the Lamè constants (λ-λ)(μ-μ)≥0, we show thatDis uniquely determined by the complete knowledge of the Dirichlet-to-Neumann map. We also obtain an uniqueness result for the monotone case from one boundary measurement.
AB - Let Ω be a bounded domain inRnwithC2-boundary and letDbe a Lipschitz domain withD⊂Ω. We consider the inverse problem (determiningD) to the system of linear elasticityDi((μD(δijδrs+δirδjs)+λDδirδjs)Djus)=0in Ω,where μD=μχD+μχRn\Dand λD=λχD+λχRn\D. Under the condition on the Lamè constants (λ-λ)(μ-μ)≥0, we show thatDis uniquely determined by the complete knowledge of the Dirichlet-to-Neumann map. We also obtain an uniqueness result for the monotone case from one boundary measurement.
UR - http://www.scopus.com/inward/record.url?scp=0031274104&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0031274104&partnerID=8YFLogxK
U2 - 10.1006/jmaa.1997.5656
DO - 10.1006/jmaa.1997.5656
M3 - Article
VL - 215
SP - 514
EP - 531
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -