Uniqueness of minimizers of weighted least gradient problems arising in hybrid inverse problems
Uniqueness of minimizers of weighted least gradient problems arising in hybrid inverse problems
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DOI：
10.1007/s00526-017-1274-x
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发表时间：
2018-02
影响因子：
2.1
通讯作者：
Amir Moradifam;A. Nachman;A. Tamasan
中科院分区：
文献类型：
--
作者：
Amir Moradifam;A. Nachman;A. Tamasan
本文研究了加权最小梯度问题$$\开始{aligned} \min \left\{ \int _{\Omega }的极小解的唯一性问题|DV|_a：v\in BV_{loc}（\Omega {\setminus } S），\; v|_{\partial \Omega }= f \right\}，\end{aligned}$$其中是相对于权重函数a的总变差，是函数a的零点集。与以前的结果相比，它假设的重量是有界远离零，这里只假设是连续的，并允许消失，也是不连续的某些子集。我们假设存在极小化子。这个问题自然出现在成像电导率从内部知识的大小的一个电流密度矢量场，其中存在的最小化是已知的先验的混合逆问题。
We study the question of uniqueness of minimizers of the weighted least gradient problem $$\begin{aligned} \min \left\{ \int _{\Omega }|Dv|_a : v\in BV_{loc}(\Omega {\setminus } S),\; v|_{\partial \Omega }= f \right\} , \end{aligned}$$whereis the total variation with respect to the weight functionaandSis the set of zeros of the functiona. In contrast with previous results, which assume that the weightand is bounded away from zero, hereais only assumed to be continuous, and is allowed to vanish and also be discontinuous in certain subsets of. We assume instead existence of aminimizer. This problem arises naturally in the hybrid inverse problem of imaging electric conductivity from interior knowledge of the magnitude of one current density vector field, where existence of aminimizer is known a priori.