与Gauss测度有关的椭圆方程比较结果中等号成立的条件

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

中文关键词:  比较结果  等号  重排  Gauss测度  椭圆方程.

英文关键词:comparison results  equalities  rearrangements  Gauss measure  elliptic equation.

中文摘要:

      本文研究了与Gauss测度有关的线性椭圆型方程比较结果的逆问题.即在文献[14]证明的不等式中,我们研究其等号的情况并且证明了等号仅在“对称”情形成立,从而得到了[14]中不等式的最优性.

英文摘要:

      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.