Continuous rearrangement and symmetry of solutions of elliptic problems
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 \(W^{1,p}\). 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.
scientific article; zbMATH DE number 1471243
scientific article