The Calderon problem for conormal potentials, I: Global uniqueness and reconstruction
偏微分方程分析
2007-05-23 v2 数学物理
math.MP
摘要
In dimensions greater than or equal to three, we establish global uniqueness and obtain reconstruction in the Calderon problem for the Schrodinger equation with certain singular potentials. The potentials considered are conormal of order less than 1-k with respect to submanifolds (of arbitrary codimension k). This gives positive results for (conormal) conductivities which are Holder of any order > 1. A related problem for highly singular potentials is shown to exhibit nonuniqueness.
引用
@article{arxiv.math/0112130,
title = {The Calderon problem for conormal potentials, I: Global uniqueness and reconstruction},
author = {Allan Greenleaf and Matti Lassas and Gunther Uhlmann},
journal= {arXiv preprint arXiv:math/0112130},
year = {2007}
}
备注
Final revision with corrections; 23 pages; to appear in Comm. Pure Appl. Math