Comparison Results for a class of Neumann Problems of the $p$-Laplace Equation on Riemannian Manifolds

Wentao Liu; Anqiang Zhu

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arXiv · 2606.22854

Comparison Results for a class of Neumann Problems of the $p$-Laplace Equation on Riemannian Manifolds

Wentao Liu·Anqiang Zhu

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Abstract

We consider Neumann boundary value problems for the $p$-Laplace equation on Riemannian manifolds with nonnegative Ricci curvature. Using spherical symmetrization under appropriate constraints, we derive Talenti-type comparison results in Lorentz spaces. We further show that, in contrast to the Robin case, the Neumann setting admits weaker constraints, which yields stronger comparison principles.

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Wentao Liu, Anqiang Zhu. 2026-06-22. Comparison Results for a class of Neumann Problems of the $p$-Laplace Equation on Riemannian Manifolds. https://arxiv.org/abs/2606.22854

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