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IOP Publishing, Nonlinearity, 3(27), p. 435-465, 2014

DOI: 10.1088/0951-7715/27/3/435

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Branches of non-symmetric critical points and symmetry breaking in nonlinear elliptic partial differential equations

Journal article published in 2014 by Jean Dolbeault ORCID, Maria J. Esteban
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This paper is available in a repository.

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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.