Branches of non-symmetric critical points and symmetry breaking in nonlinear elliptic partial differential equations
Analysis of PDEs
2014-03-05 v2
Abstract
In this paper we study the bifurcation of branches of non-symmetric solutions from the symmetric branch of solutions to the Euler-Lagrange equations satisfied by optimal functions in functional inequalities of Caffarelli-Kohn-Nirenberg type. We establish the asymptotic behavior of the branches for large values of the bifurcation parameter. We also perform an expansion in a neighborhood of the first bifurcation point on the branch of symmetric solutions, that characterizes the local behavior of the non-symmetric branch. These results are compatible with earlier numerical and theoretical observations. Further numerical results allow us to distinguish two global scenarios. This sheds a new light on the symmetry breaking phenomenon.
Keywords
Cite
@article{arxiv.1304.4000,
title = {Branches of non-symmetric critical points and symmetry breaking in nonlinear elliptic partial differential equations},
author = {Jean Dolbeault and Maria J. Esteban},
journal= {arXiv preprint arXiv:1304.4000},
year = {2014}
}