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The Liouville property and a conjecture of De Giorgi

✍ Scribed by Martin T. Barlow; Richard F. Bass; Changfeng Gui

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 382 KB
Volume: 53
Category: Article
ISSN: 0010-3640
DOI: 10.1002/1097-0312(200008)53:8<1007::aid-cpa3>3.0.co;2-u

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✦ Synopsis

We consider bounded entire solutions of the nonlinear PDE ∆u + uu 3 = 0 in R d and prove that under certain monotonicity conditions these solutions must be constant on hyperplanes. The proof uses a Liouville theorem for harmonic functions associated with a nonuniformly elliptic divergence form operator.

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