论文标题
非线性磁性schrödinger方程的反问题
Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds
论文作者
论文摘要
我们研究了非线性磁性schrödinger操作员的逆边界问题，在二维$ n \ ge 3 $的横向各向异性riemannian歧管上。在对非线性的合适假设下，我们表明，在歧管边界上的dirichlet到neumann图的知识决定了非线性磁和电势。在此结果中，没有对横向歧管的假设，而线性磁性schrödinger操作员的相应逆边界问题在此通用性中仍然是打开的。
We study the inverse boundary problem for a nonlinear magnetic Schrödinger operator on a conformally transversally anisotropic Riemannian manifold of dimension $n\ge 3$. Under suitable assumptions on the nonlinearity, we show that the knowledge of the Dirichlet-to-Neumann map on the boundary of the manifold determines the nonlinear magnetic and electric potentials uniquely. No assumptions on the transversal manifold are made in this result, whereas the corresponding inverse boundary problem for the linear magnetic Schrödinger operator is still open in this generality.
