Comparison results for Poisson equation with mixed boundary condition on manifolds

2021/10/13 by Haiqing Cheng, Tengfei Ma, Cheng, Haiqing +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2110.06814

openalex publication_date 2021/10/13 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28

Abstract

In this article, we establish a L¹ estimate for solutions to Poisson equation with mixed boundary condition, on complete noncompact manifolds with nonnegative Ricci curvature and compact manifolds with positive Ricci curvature respectively. On Riemann surfaces we obtain a Talenti-type comparison. Our results generalize main theorems in [2] to Riemannian setting, and Chen-Li's result [8] to the case of variable Robin parameter.

Citations

• A Talenti comparison result for solutions to elliptic problems with Robin boundary conditions

Cited by

• Schwarz symmetrizations in parabolic equations on complete manifolds

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