Entire Solutions of the Allen-cahn Equation and Complete Embedded Minimal Surfaces
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چکیده
We review some recent results on construction of entire solutions to the classical semilinear elliptic equation ∆u+u−u = 0 in R . In various cases, large dilations of an embedded, complete minimal surface approximate the transition set of a solution that connects the equilibria ±1. In particular, our construction answers negatively a celebrated conjecture by E. De Giorgi in dimensions N ≥ 9.
منابع مشابه
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تاریخ انتشار 2009