Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds

被引：1

作者：

Chen, Daguang ^{[1
]}

Li, Haizhong ^{[1
]}

Wei, Yilun ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2023年 / 34卷 / 08期

关键词：

Bossel-Daners inequality; isoperimetric inequality; Talenti's comparison; Lorentz norm; FABER-KRAHN INEQUALITY;

D O I：

10.1142/S0129167X23500453

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, by using Schwarz rearrangement and isoperimetric inequalities, we prove comparison results for the solutions of Poisson equations on complete Riemannian man-ifolds with Ric = (n- 1)?, ? = 0 or 1, which extends the results in [A. Alvino, C. Nitsch and C. Trombetti, A Talenti comparison result for solutions to elliptic problems with Robin boundary conditions, Comm. Pure Appl. Math. 76(3) (2023) 585-603]. Further-more, as applications of our comparison results, we obtain the Saint-Venant inequality and Bossel-Daners inequality for Robin Laplacian.

引用

页数：19

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