| On the Case of Equalities in Comparison Results for Elliptic Equations Related to Gauss Measure |
| Received:April 13, 2010 Revised:May 28, 2010 |
| Key Words:
comparison results equalities rearrangements Gauss measure elliptic equation.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10401009) and the Program for New Century Excellent Talents in University (Grant No.060275). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.05.001 |
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