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

par Bonheure, Denis ;Hamel, François
Référence Chinese annals of mathematics. Ser. B, 38, 1, page (149-172)
Publication Publié, 2017-01

Article révisé par les pairs

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Résumé :

In this paper, the authors prove an analogue of Gibbons’ conjecture for the extended fourth order Allen-Cahn equation in ℝN, 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.