One-dimensional symmetry and Liouville ...
Document type :
Compte-rendu et recension critique d'ouvrage
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]
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
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
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 >
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 :
Comment :
Dedicated to Haïm Brezis with deep admiration.
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