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Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds
Published 12 Oct 2021 in math.DG and math.AP | (2110.06005v1)
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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