Radial symmetry and symmetry breaking for some interpolation inequalities

About existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalities

Symmetry, Symmetry Breaking and Topology

The ground state of a system with symmetry can be described by a group G. This symmetry groupG can be discrete or continuous. Thus for a crystalG is a finite group while for the vacuum state of a grand unified theory G is a continuous Lie group. The ground state symmetry described by G can change spontaneously from G to one of its subgroups H as the external parameters of the system are modifie...

A scenario for symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities

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 admi...

Symmetry and Symmetry Breaking in Electrostatic MEMS

The use of electrostatic forces to provide actuation is a method of central importance in microelectromechanical systems (MEMS) and is of growing importance in nanoelectromechanical systems (NEMS). The study of electrostatic actuation has led to numerous interesting experimental, theoretical, and numerical results. Yet, surprisingly, even simple electrostatically actuated systems have secrets t...

Chiral Symmetry and Chiral Symmetry Breaking*

Lectures presented at the session on " Recent Developments in Quantum Field Theory and Statistical Mechanics " of the Les Houches Summer School of Theoretical Physics August 1982 *Nork supported by the