论文标题
通过Riemannian歧管上的弹性Dirichlet到Neumann地图确定LAMé系数
Determining Lamé coefficients by elastic Dirichlet-to-Neumann map on a Riemannian manifold
论文作者
论文摘要
对于Lamé运算符$ \ Mathcal {l} _ {λ，μ} $，具有可变系数$λ$和$μ$的$λ$和$μ$，带有光滑的Riemannian歧管$（m，g），带有光滑的边界$ \ partial m $，我们给出了全部符号，以表达完整的表达式，以表达完整的dirostic dirostic diriclet to dire dire diremann to umann to umann nneymann $λ。我们表明，$λ_{λ，μ} $唯一确定$ \ partial m $上的lamé系数的所有订单的部分衍生物。此外，对于非空的开放子集$γ\ subset \ partial m $，假设歧管和lamé系数是真正的分析性最高为$γ$，我们证明$λ_{λ_，λ，μ} $唯一确定整个级别的lamé系数在整个级别$ \ bar bar {m} $上。
For the Lamé operator $\mathcal{L}_{λ,μ}$ with variable coefficients $λ$ and $μ$ on a smooth compact Riemannian manifold $(M,g)$ with smooth boundary $\partial M$, we give an explicit expression for full symbol of the elastic Dirichlet-to-Neumann map $Λ_{λ,μ}$. We show that $Λ_{λ,μ}$ uniquely determines partial derivatives of all orders of the Lamé coefficients $λ$ and $μ$ on $\partial M$. Moreover, for a nonempty open subset $Γ\subset\partial M$, suppose that the manifold and the Lamé coefficients are real analytic up to $Γ$, we prove that $Λ_{λ,μ}$ uniquely determines the Lamé coefficients on the whole manifold $\bar{M}$.
