LOG-CONCAVITY OF THE FIRST DIRICHLET EIGENFUNCTION OF SOME ELLIPTIC DIFFERENTIAL OPERATORS AND CONVEXITY INEQUALITIES FOR THE RELEVANT EIGENVALUE  

作　　者：Andrea COLESANTI 

机构地区：[1]Dipartimento di Matematica&Informdtica‘U.Dini’,Universitàdegli Studi di Firenze,Viale Morgagni 67/A-50134,Firenze,Italy

出　　处：《Acta Mathematica Scientia》2025年第1期143-152,共10页数学物理学报(B辑英文版)

基　　金：supported by the project Disuguaglianze analitiche e geometriche,funded by the Gruppo per Analisi Matematica la Probabilitàe le loro Applicazioni.

摘　　要：Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.

关 键 词：EIGENVALUE LOG-CONCAVITY elliptic operator Brunn-Minkowski inequality convex body 

分 类 号：O186.5[理学—数学]