论文标题
半线性椭圆PDE的逆问题，单点测量
Inverse problems for semilinear elliptic PDE with measurements at a single point
论文作者
论文摘要
我们考虑了从Dirichlet到Neumann图的知识中确定半线性椭圆方程中潜力的反问题。对于有界的欧几里得域，我们证明电势是由在单个边界点测得的dirichlet到neumann映射唯一决定的，或者是按固定度量集成的。即使仅在边界的一小部分中给出DIRICHLET数据，该结果也是有效的。我们还为Riemannian流形提供了相关的唯一性结果。
We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the Dirichlet-to-Neumann map measured at a single boundary point, or integrated against a fixed measure. This result is valid even when the Dirichlet data is only given on a small subset of the boundary. We also give related uniqueness results on Riemannian manifolds.
