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arXiv · 1503.09032

Harnack inequality for degenerate and singular operators of $p$-Laplacian type on Riemannian manifolds

Soojung Kim
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Abstract

We study viscosity solutions to degenerate and singular elliptic equations of $p$-Laplacian type on Riemannian manifolds. The Krylov-Safonov type Harnack inequality for the $p$-Laplacian operators with $1<p<\infty$ is established on the manifolds with Ricci curvature bounded from below based on ABP type estimates. We also prove the Harnack inequality for nonlinear $p$-Laplacian type operators assuming that a nonlinear perturbation of Ricci curvature is bounded below.

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Soojung Kim. 2015-03-31. Harnack inequality for degenerate and singular operators of $p$-Laplacian type on Riemannian manifolds. https://arxiv.org/abs/1503.09032

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