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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Kim, S. Harnack inequality for degenerate and singular operators of p-Laplacian type on Riemannian manifolds. Math. Ann. 366, 1721–1785 (2016). https://doi.org/10.1007/s00208-016-1372-7
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DOI: https://doi.org/10.1007/s00208-016-1372-7