New realization of the pseudoconvexity and its application to an inverse problem
New realization of the pseudoconvexity and its application to an inverse problem
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伪凸性的新认识及其在反问题中的应用
DOI：
10.1080/00036810802428995
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发表时间：
2009
影响因子：
1.1
通讯作者：
Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
O. Imanuvilov;V. Isakov;Masahiro Yamamoto
考虑一类具有可变主项的双曲型微分算子。我们首先给出了伪凸性的一个充分条件和一个必要条件。我们的充分条件意味着Carleman估计中的权函数生成的水平集相对于a 0（x）给出的射线集是凸的，并且给出了一个更一般的明确的伪凸性条件a 0。第二，我们应用Carleman估计的反问题，确定一个0的柯西数据的横向边界上的放松约束0。
We consider a hyperbolic differential operator with variable principal term. We first give a sufficient condition for the pseudoconvexity which yields a Carleman estimate and a necessary condition. Our sufficient condition implies that level sets generated by the weight function in the Carleman estimate are convex with respect to the set of rays given by a 0(x), and give a more general explicit condition of a 0 for the pseudoconvexity. Second we apply the Carleman estimate to an inverse problem of determining a 0 by Cauchy data on a lateral boundary with relaxed constraints on a 0.