Abstract
We consider the entire graph S of a continuous real function over R N − 1 with N ⩾ 3 . Let Ω be a domain in R N with S as a boundary. Consider in Ω the heat flow with initial temperature 0 and boundary temperature 1. The problem we consider is to characterize S in such a way that there exists a stationary isothermic surface in Ω. We show that S must be a hyperplane under some general conditions on S. This is related to Liouville or Bernstein-type theorems for some elliptic Monge–Ampère-type equation.
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