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One-Dimensional Symmetry and Liouville Type Results for the Fourth Order Allen-Cahn Equation in RN |
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| Authors: | Denis BONHEURE and Fran{c{c}}ois HAMEL |
| Affiliation: | 1. Département de Mathématique, Université libre de Bruxelles, CP 214, Boulevard du Triomphe, B-1050 Bruxelles, Belgium and INRIA-Team MEPHYSTO;2. Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France |
| Abstract: | In this paper, the authors 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. The authors also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities. |
| Keywords: | Fourth order elliptic equation Allen-Cahn equation Extended Fisher-Kolmogorov equation One-dimensional symmetry Liouville type results |
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