Abstract
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.
Original language | English |
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Pages (from-to) | 931-946 |
Number of pages | 16 |
Journal | Annals of Mathematics |
Volume | 156 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2002 Nov |
Externally published | Yes |
Keywords
- Heat equation
- Overdetermined problems
- Stationary surfaces
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty