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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics