Symmetrizations are a tool used to prove that solutions of variational problems are symmetrical. To every function \(u\), a more symmetrical fonction \(u^*\) is associated. This nonlinear transformation preserves the measure of sublevel sets, so that many integral functionals are preserved or decrease when the function they contain is symmetrized.

I have worked on

• the relationships between the properties of the symmetrization of sets and the symmetrization of functions,
• the approximation of symmetrizations by simpler symmetrizations, by simpler symmetrizations, in particular by polarizations, and random approximation,
• the symmetry of critical points obtained by minimax methods (Mountain Pass Theorem, Linking Theorem, Krasnsoselskii genus),
• anisotropic symmetrizations, i.e. symmetrization with respect to a noneuclidean norm.