Continuous rearrangement and symmetry of solutions of elliptic problems
type: Item
instance of: scholarly article
title: Continuous rearrangement and symmetry of solutions of elliptic problems
zbMATH Open document ID: 0965.49002
DOI: 10.1007/BF02829490
author: Friedemann Brock
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2000-11-22T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 1471243
zbMATH Keywords: continuous Steiner symmetrization
zbMATH Keywords: integral inequality
zbMATH Keywords: Dirichlet-type integral
zbMATH Keywords: semilinear elliptic problem
zbMATH Keywords: symmetry of solutions
zbMATH Keywords: rearrangement
zbMATH Keywords: minimizers
zbMATH Keywords: variational problems
reviewed by: P. Neittaanmäki
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1471243