On the Case of Equalities in Comparison Results for Elliptic Equations Related to Gauss Measure

摘要

In this paper,we deal with a Dirichlet problem for linear elliptic equations related to Gauss measure.For this problem,we study the converse of some inequalities proved by other authors,in the sense that we study the case of equalities and show that equalities are achieved only in the "symmetrized" situations.In addition,under other assumptions,we give a different form of comparison results and discuss the corresponding case of equalities.