A scenario for symmetry breaking in Caffarelli–Kohn–Nirenberg inequalities
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J. Dolbeault
und
M. J. Esteban
Abstract
-The purpose of this paper is to explain the phenomenon of symmetry breaking for optimal functions in functional inequalities by the numerical computations of some well chosen solutions of the corresponding Euler-Lagrange equations. For many of those inequalities it was believed that the only source of symmetry breaking would be the instability of the symmetric optimizer in the class of all admissible functions. But recently, it was shown by an indirect argument that for some Caffarelli-Kohn-Nirenberg inequalities this conjecture was not true. In order to understand this new symmetry breaking mechanism we have computed the branch of minimal solutions for a simple problem. A reparametrization of this branch allows us to build a scenario for the new phenomenon of symmetry breaking. The computations have been performed using freefem++.
© 2013 by Walter de Gruyter GmbH & Co.
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- Masthead
- Preface
- A non-standard FETI-DP mortar method for Stokes problem
- Implementation of a low order mimetic elements in freefem++
- Moving meshes with freefem++
- Mathematical modeling of heat treatment for a steering rack including mechanical effects
- A scenario for symmetry breaking in Caffarelli–Kohn–Nirenberg inequalities
- New development in freefem++
- Fictitious domain method to model a movable rigid body in a sound wave
- High performance domain decomposition methods on massively parallel architectures with freefem++
- Solution of 2D Boussinesq systems with freefem++: the flat bottom case
- A finite element BFGS algorithm for the reconstruction of the flow field generated by vortex rings
- Author Index
Artikel in diesem Heft
- Masthead
- Preface
- A non-standard FETI-DP mortar method for Stokes problem
- Implementation of a low order mimetic elements in freefem++
- Moving meshes with freefem++
- Mathematical modeling of heat treatment for a steering rack including mechanical effects
- A scenario for symmetry breaking in Caffarelli–Kohn–Nirenberg inequalities
- New development in freefem++
- Fictitious domain method to model a movable rigid body in a sound wave
- High performance domain decomposition methods on massively parallel architectures with freefem++
- Solution of 2D Boussinesq systems with freefem++: the flat bottom case
- A finite element BFGS algorithm for the reconstruction of the flow field generated by vortex rings
- Author Index
