Isoperimetric inequalities for -Hessian equations

Advances in Nonlinear Analysis

article

Ahmed Mohammed¹  Giovanni Porru²  Abdessalam Safoui³ 

[1] Department of Mathematical Sciences, Ball State University;Department of Mathematics and Informatics, University of Cagliari;Department of Mathematics, University of Marrakesh

关键词: Monge–Ampère type equations;    rearrangements;    eigenvalues;    isoperimetric inequalities;   

DOI  :  10.1515/anona-2011-0006

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Abstract. We consider the homogeneous Dirichlet problem for a special -Hessian equation of sub-linear type in a -convex domain , . We study the comparison between the solution of this problem and the (radial) solution of the corresponding problem in a ball having the same -quermassintegral as . Next, we consider the eigenvalue problem for the -Hessian equation and study a comparison between its principal eigenfunction and the principal eigenfunction of the corresponding problem in a ball having the same -quermassintegral as . Symmetrization techniques and comparison principles are the main tools used to get these inequalities.

【 授权许可】

CC BY