An inverse problem for the magnetic Schrödinger equation and quasi-exponential solutions of nonsmooth partial differential equations
An inverse problem for the magnetic Schrödinger equation and quasi-exponential solutions of nonsmooth partial differential equations
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磁薛定谔方程的反问题和非光滑偏微分方程的拟指数解
DOI：
10.1088/0266-5611/18/5/314
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发表时间：
2002
期刊：
影响因子：
2.1
通讯作者：
A. Panchenko
中科院分区：
文献类型：
--
作者：
A. Panchenko
我们研究的反问题的Schr？有界Lipschitz域上的dinger方程? Rn，n？3当磁势和电势都存在时。我们证明，发散的磁势A和电势q的自由分量可以唯一地恢复从狄利克雷到诺依曼地图提供AL？(?) n，q L？(?), A的无发散部分的法向分量在？？上为零，和||一||?（1 +直径（？））足够小。为了证明唯一性，我们构造特殊的椭圆型方程的形式？u + B？? u + cu = 0，假设B L？(?) n，c L？(?),并且B足够小。
We study an inverse problem for the Schr?dinger equation in a bounded Lipschitz domain ? ? Rn, n ? 3 when both magnetic and electric potentials are present. We prove that the divergence-free component of the magnetic potential A and the electric potential q can be uniquely recovered from the Dirichlet-to-Neumann map provided A L? (?)n, q L? (?), the normal component of the divergence-free part of A is zero on ??, and ||A||? (1 + diam (?)) is sufficiently small. In order to prove uniqueness, we construct special quasi-exponential solutions for elliptic equations of the form ?u + b ? ?u + cu = 0, assuming that b L? (?)n, c L? (?), and b is sufficiently small.