论文标题
跨数据的部分数据逆问题逆问题
Partial data inverse problems for quasilinear conductivity equations
论文作者
论文摘要
我们表明，在$ \ mathbb {r}^n $，$ n \ ge 2 $中，对平滑域边界的任意开放的非空域边界边界上给出的dirichlet到neumann地图的知识是针对半线性和Quasilineartioneartivation等级的，确定了非线性电导率。证明中的主要成分是一定的$ l^1 $密度结果，涉及谐波功能梯度的产物总和，这些梯度在边界的封闭适当子集上消失。
We show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in $\mathbb{R}^n$, $n\ge 2$, for classes of semilinear and quasilinear conductivity equations, determines the nonlinear conductivities uniquely. The main ingredient in the proof is a certain $L^1$-density result involving sums of products of gradients of harmonic functions which vanish on a closed proper subset of the boundary.
