Comparison results for Poisson equation with mixed boundary condition on manifolds

Abstract

In this article, we establish a $L^1$ 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.

All comments are welcome! In this version, we corrected some typos

References in corpus (1)

• Talenti's comparison theorem for Poisson equation and applications on Riemannian manifold with nonnegative Ricci curvature

Cited by in corpus (1)

• Schwarz symmetrizations in parabolic equations on complete manifolds