Continuous rearrangement and symmetry of solutions of elliptic problems |
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Authors: | Friedemann Brock |
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Institution: | (1) Department of Mathematics, Univeristy of Missouri-Columbia, 65211 Columbia, MO, USA |
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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 spacesW
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. |
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Keywords: | Continuous symmetrization integral inequality Dirichlet-type integral semilinear elliptic problem symmetry of the solution |
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