One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in R$^N$

Denis Bonheure 1, 2 François Hamel 3
1 MEPHYSTO - Quantitative methods for stochastic models in physics
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : In this paper, we prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R N , as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. We also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities.
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https://hal.archives-ouvertes.fr/hal-01182688
Contributor : Francois Hamel <>
Submitted on : Sunday, August 2, 2015 - 12:13:48 AM
Last modification on : Monday, March 4, 2019 - 2:04:17 PM
Long-term archiving on : Tuesday, November 3, 2015 - 2:52:18 PM

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  • HAL Id : hal-01182688, version 1
  • ARXIV : 1508.00333

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Denis Bonheure, François Hamel. One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in R$^N$. Chinese Annals of Mathematics - Series B, Springer Verlag, 2016, pp.25. ⟨hal-01182688v1⟩

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