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arXiv · 2110.06005

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

Daguang Chen·Haizhong Li·Yilun Wei
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Abstract

In this paper, by using Schwarz rearrangement and isoperimetric inequalities, we prove comparison results for the solutions of Poisson equations on complete Riemannian manifolds with $Ric\geq (n-1)\kappa$, $\, \kappa\geq 0$, which extends the results in \cite{ANT-Talenti-a}. Furthermore, as applications of our comparison results, we obtain the Saint-Venant inequality and Bossel-Daners inequality for Robin Laplacian.

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Daguang Chen, Haizhong Li, Yilun Wei. 2021-10-12. Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds. https://arxiv.org/abs/2110.06005

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