DOUBLING INEQUALITIES FOR THE LAME SYSTEM WITH ROUGH COEFFICIENTS

作者：Koch Herbert^*; Lin Ching Lung; Wang Jenn Nan

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144(12): 5309-5318.

DOI：10.1090/proc/13175

• Elliptic systems
• doubling
• Carleman inequalities
• quantitative uniqueness

In this paper we study the local behavior of a solution to the Lame system when the Lame coefficients lambda and mu satisfy that mu is Lipschitz and lambda is essentially bounded in dimension n >= 2. One of the main results is the local doubling inequality for the solution of the Lame 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.

• 出版日期2016-12