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Continuous rearrangement and symmetry of solutions of elliptic problems

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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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  1. Department of Mathematics, Univeristy of Missouri-Columbia, 65211, Columbia, MO, USA

    Friedemann Brock

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  1. Friedemann Brock
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Brock, F. Continuous rearrangement and symmetry of solutions of elliptic problems. Proc. Indian Acad. Sci. (Math. Sci.) 110, 157–204 (2000). https://doi.org/10.1007/BF02829490

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