Continuous Rearrangement and Symmetry of Solutions of Elliptic Problems

Proceedings Mathematical Sciences

Friedemann Brock¹ 

[1] Department of Mathematics, Univeristy of Missouri-Columbia, Columbia MO , USA$$

关键词: Continuous symmetrization;    integral inequality;    Dirichlet-type integral;    semilinear elliptic problem;    symmetry of the solution.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 𝑊1, 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.

【 授权许可】

Unknown