Abstract
In this paper we study the local behavior of a solution to the Lamé system when the Lamé coefficients λ and μ satisfy that μ is Lipschitz and λ is essentially bounded in dimension n ≥ 2. One of the main results is the local doubling inequality for the solution of the Lamé system. This is a quantitative estimate of the strong unique continuation property. Our proof relies on Carleman estimates with carefully chosen weights. Furthermore, we also prove the global doubling inequality, which is useful in some inverse problems.
| Original language | English |
|---|---|
| Pages (from-to) | 5309-5318 |
| Number of pages | 10 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 144 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2016 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
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Doubling inequalities for the lamé system with rough coefficients. / Koch, Herbert; Lin, Ching Lung; Wang, Jenn Nan.
In: Proceedings of the American Mathematical Society, Vol. 144, No. 12, 01.01.2016, p. 5309-5318.Research output: Contribution to journal › Article
TY - JOUR
T1 - Doubling inequalities for the lamé system with rough coefficients
AU - Koch, Herbert
AU - Lin, Ching Lung
AU - Wang, Jenn Nan
PY - 2016/1/1
Y1 - 2016/1/1
N2 - In this paper we study the local behavior of a solution to the Lamé system when the Lamé coefficients λ and μ satisfy that μ is Lipschitz and λ is essentially bounded in dimension n ≥ 2. One of the main results is the local doubling inequality for the solution of the Lamé system. This is a quantitative estimate of the strong unique continuation property. Our proof relies on Carleman estimates with carefully chosen weights. Furthermore, we also prove the global doubling inequality, which is useful in some inverse problems.
AB - In this paper we study the local behavior of a solution to the Lamé system when the Lamé coefficients λ and μ satisfy that μ is Lipschitz and λ is essentially bounded in dimension n ≥ 2. One of the main results is the local doubling inequality for the solution of the Lamé system. This is a quantitative estimate of the strong unique continuation property. Our proof relies on Carleman estimates with carefully chosen weights. Furthermore, we also prove the global doubling inequality, which is useful in some inverse problems.
UR - http://www.scopus.com/inward/record.url?scp=84992393681&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84992393681&partnerID=8YFLogxK
U2 - 10.1090/proc/13175
DO - 10.1090/proc/13175
M3 - Article
AN - SCOPUS:84992393681
VL - 144
SP - 5309
EP - 5318
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 12
ER -