Matzoh ball soup: Heat conductors with a stationary isothermic surface

• 成果类型: Article
• 署名作者: Magnanini, R; Sakaguchi, S
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3597287
• 发表日期: 2002
• 页码: 931-946
• 关键词: spatial critical-points; FLOW; EQUATIONS

摘要

We consider a bounded heat conductor that satisfies the exterior sphere condition. Suppose that, initially, the conductor has temperature 0 and, at all times, its boundary is kept at temperature 1. We show that if the conductor contains a proper sub-domain, satisfying the interior cone condition and having constant boundary temperature at each given time, then the conductor must be a ball.