Doubling inequalities for the lamé system with rough coefficients

Herbert Koch; Ching Lung Lin; Jenn Nan Wang

doi:10.1090/proc/13175

Doubling inequalities for the lamé system with rough coefficients

Herbert Koch, Ching Lung Lin, Jenn Nan Wang

Department of Mathematics

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

6 Citations (Scopus)

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	https://doi.org/10.1090/proc/13175
Publication status	Published - 2016

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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title = "Doubling inequalities for the lam{\'e} system with rough coefficients",

abstract = "In this paper we study the local behavior of a solution to the Lam{\'e} system when the Lam{\'e} 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 Lam{\'e} 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.",

author = "Herbert Koch and Lin, {Ching Lung} and Wang, {Jenn Nan}",

note = "Funding Information: The first author was partially supported by the DFG through SFB 1060. The second author was partially supported by the Ministry of Science and Technology of Taiwan. The third author was partially supported by MOST102-2115-M-002-009-MY3.",

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T1 - Doubling inequalities for the lamé system with rough coefficients

AU - Koch, Herbert

AU - Lin, Ching Lung

AU - Wang, Jenn Nan

N1 - Funding Information: The first author was partially supported by the DFG through SFB 1060. The second author was partially supported by the Ministry of Science and Technology of Taiwan. The third author was partially supported by MOST102-2115-M-002-009-MY3.

PY - 2016

Y1 - 2016

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.

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