Continuous rearrangement and symmetry of solutions of elliptic problems

  • Friedemann Brock
Article

DOI: 10.1007/BF02829490

Cite this article as:
Brock, F. Proc. Indian Acad. Sci. (Math. Sci.) (2000) 110: 157. doi:10.1007/BF02829490

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 spacesW1,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.

Keywords

Continuous symmetrizationintegral inequalityDirichlet-type integralsemilinear elliptic problemsymmetry of the solution

Copyright information

© Indian Academy of Sciences 2000

Authors and Affiliations

  • Friedemann Brock
    • 1
  1. 1.Department of MathematicsUniveristy of Missouri-ColumbiaColumbiaUSA