Uniqueness in the two-dimensional inverse conductivity problems of determining convex polygonal supports: case of variable conductivity
Uniqueness in the two-dimensional inverse conductivity problems of determining convex polygonal supports: case of variable conductivity
复制标题
确定凸多边形支撑的二维反电导率问题的唯一性：可变电导率的情况
DOI：
10.1088/0266-5611/20/2/012
复制
发表时间：
2004
期刊：
影响因子：
2.1
通讯作者：
Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
Sungwhan Kim;Masahiro Yamamoto
在有界域中，我们考虑div((L(X)+m(X)χD(X))∇u(X))+k(X)u(X)=0，其中满足L，L+m>；0上，子域D是有限个多边形的并，χD表示D和k L∞(Ω的特征函数，k≥0上。我们讨论了由u的边界数据确定D的反问题。我们的主要结果如下。(I)情形k≡0：适当地给出∂Ω上u的单个Dirichlet基准，得到D的凸包的唯一性。(Ii)情形0<；k(X)<；λ0，其中λ0是L的最小值与−Δ的第一本征值与零Dirichlet边界条件的乘积。通过在∂Ω上两次适当地将Dirichlet输入改为u，得到的两个诺依曼数据保证了凸壳的唯一性。
In a bounded domain , we consider div((l(x) + m(x)χD(x))∇u(x)) + k(x)u(x) = 0, where satisfy l, l + m > 0 on , the subdomain D is the union of a finite number of polygons, χD denotes the characteristic function of D and k L∞(Ω), k ≥ 0 on . We discuss an inverse problem of determining D by the boundary data of u. Our main results are stated as follows. (i) Case k ≡ 0: a suitably given single Dirichlet datum of u on ∂Ω yields the uniqueness of the convex hull of D. (ii) Case 0 < k(x) < λ0, where λ0 is the product of the minimum of l and the first eigenvalue of −Δ with the zero Dirichlet boundary condition. By changing Dirichlet inputs to u on ∂Ω twice and suitably, the resulting two Neumann data guarantee the uniqueness of the convex hull.