论文标题
表征障碍问题中紧凑的巧合集 - 简短的证明
Characterizing compact coincidence sets in the obstacle problem -- a short proof
论文作者
论文摘要
由几乎完全开放的问题的动机，即在更高维度中表征无限的经典障碍物问题的全球解决方案集合集合，我们在本说明中给出了一个简洁且易于扩展的证据，证明了已知的事实，即如果重合集合$ \ = 0 \ = 0 \ = 0 \ \}全球解决方案$ u $ u $ u $ unbient y ablenty Interior Intior Itior IT EllipsoiD是Ellipsoid的。
Motivated by the almost completely open problem of characterizing unbounded coincidence sets of global solutions of the classical obstacle problem in higher dimensions, we give in this note a concise and easy-to-extend proof of the known fact that if the coincidence set $\{u=0 \}$ of a global solution $u$ is bounded with nonempty interior then it is an ellipsoid.
