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 in...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.展开更多
基金carried out in the framework of the Labex Archimède(ANR-11-LABX-0033)the A*MIDEX project(ANR-11-IDEX-0001-02)+6 种基金funded by the "Investissements d’Avenir" French Government program managed by the French National Research Agency(ANR)funding from the European Research Council under the European Union’s Seventh Framework Programme(FP/2007-2013)ERC Grant Agreement n.321186-ReaDiReaction-Diffusion Equations,Propagation and Modelling and from the ANR NONLOCAL project(ANR-14-CE25-0013)supported by INRIA-Team MEPHYSTOMIS F.4508.14(FNRS)PDR T.1110.14F(FNRS)ARC AUWB-2012-12/17-ULB1-IAPAS
文摘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.
