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arXiv · 1508.00333

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

Denis Bonheure·François Hamel
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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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Denis Bonheure, François Hamel. 2016-03-11. One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in R$^N$. https://arxiv.org/abs/1508.00333

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