Complete classification of global solutions to the obstacle problem

• 成果类型: Article
• 署名作者: Eberle, Simon; Figalli, Alessio; Weiss, Georg s.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2025.201.1.3
• 发表日期: 2025
• 页码: 167-224
• 关键词: null quadrature domains; free-boundary; REGULARITY

摘要

The characterization of global solutions to the obstacle problems in RN, or equivalently of null quadrature domains, has been studied for more than 90 years. In this paper, we give a conclusive answer to this problem by proving the following long-standing conjecture: The coincidence set of a global solution to the obstacle problem is either a half-space, an ellipsoid, a paraboloid, or a cylinder with an ellipsoid or a paraboloid as base.