Symmetry and symmetry breaking: rigidity and flows in elliptic PDEs - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2017

Symmetry and symmetry breaking: rigidity and flows in elliptic PDEs

Résumé

The issue of symmetry and symmetry breaking is fundamental in all areas of science. Symmetry is often assimilated to order and beauty while symmetry breaking is the source of many interesting phenomena such as phase transitions, instabilities, segregation, self-organization, etc. In this contribution we review a series of sharp results of symmetry of nonnegative solutions of nonlinear elliptic differential equation associated with minimization problems on Euclidean spaces or manifolds. Nonnegative solutions of those equations are unique, a property that can also be interpreted as a rigidity result. The method relies on linear and nonlinear flows which reveal deep and robust properties of a large class of variational problems. Local results on linear instability leading to symmetry breaking and the bifurcation of non-symmetric branches of solutions are reinterpreted in a larger, global, variational picture in which our flows characterize directions of descent.
Fichier principal
Vignette du fichier
proc-ICM2018-6.pdf (263.11 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01651793 , version 1 (29-11-2017)

Identifiants

Citer

Jean Dolbeault, Maria J. Esteban, Michael Loss. Symmetry and symmetry breaking: rigidity and flows in elliptic PDEs. International Congress of Mathematicians, IMU, 2018, Rio de Janeiro, Brazil. pp.2279-2304, ⟨10.1142/9789813272880_0138⟩. ⟨hal-01651793⟩
322 Consultations
549 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More