Title :

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

Author(s) :

Bonheure, Denis [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de mathématiques Université Libre de Bruxelles
Hamel, François [Auteur]
Institut de Mathématiques de Marseille [I2M]

Journal title :

Chinese Annals of Mathematics - Series B
Special Issue in Honor of Haim Brezis

Pages :

149 - 172

Publisher :

Springer Verlag

Publication date :

2017-01

ISSN :

0252-9599

English keyword(s) :

Gibbons' conjecture
one-dimensional symmetry
Liouville type results
Fourth order Allen-Cahn equation

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

INITIATIVE D'EXCELLENCE AIX MARSEILLE UNIVERSITE
Phénomènes de propagation et équations non locales

Comment :

Dedicated to Haïm Brezis with deep admiration.

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL