发表机构
University of Helsinki; National Yang Ming Chiao Tung University; University of Duisburg-Essen（赫尔辛基大学; 国立阳明交通大学; 杜伊斯堡-埃森大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对带未知势的平面薛定谔方程，证明了声软障碍的单次测量唯一性，通过构造边界数据使Neumann测量值差异，利用Dirichlet-to-Neumann映射唯一确定障碍与势，无需凸性等假设。
AI 中文摘要
我们针对带有未知周围势的平面薛定谔方程中的内部声软障碍，证明了单次测量唯一性结果。对于具有不同障碍的任意两种构型，我们构造了一个边界数据，使得对应的Neumann测量值存在差异。完整的Dirichlet-to-Neumann映射可唯一确定障碍和势。障碍可包含多个连通分支，且不施加凸性或解析性假设，也无需在测量边界附近已知势。
英文摘要
We prove a single measurement uniqueness result for interior sound-soft obstacles in the planar Schrödinger equation with an unknown surrounding potential. For any two configurations with different obstacles, we construct a boundary datum for which the corresponding Neumann measurements differ. The full Dirichlet-to-Neumann map uniquely determines both the obstacle and the potential. The obstacles may have several connected components, and no convexity or analyticity assumptions are imposed. Neither potential is required to be known near the measurement boundary.
Comments20 pages
