Continuous rearrangement and symmetry of solutions of elliptic problems, Habilitation Thesis (Leipzig

Abstract. This work presents new results and applications for the continuous Steiner symmetrization. There are proved some functional inequalities, e.g. for Dirichlet-type integrals and convolutions and also continuity properties in Sobolev spaces W1;p. Further it is shown that the local minimizers of some variational problems and the nonnegative solutions of some semilinear elliptic problems in symmetric domains satisfy a weak, `local ' kind of symmetry