Title
Harnack inequality for nondivergent elliptic operators on Riemannian manifolds
Abstract
We consider second-order linear elliptic operators of nondivergence type which is intrinsically defined on Riemannian manifolds. Cabré proved a global Krylov-Safonov Harnack inequality under the assumption that the sectional curvature is nonnegative. We improve Cabré's result and, as a consequence, we give another proof to Harnack inequality of Yau for positive harmonic functions on Riemannian manifolds with nonnegative Ricci curvature using the nondivergence structure of the Laplace operator.
Related to
Institute for Mathematics and Its Applications>IMA Preprints Series
Suggested Citation
Kim, Seick.
(2002).
Harnack inequality for nondivergent elliptic operators on Riemannian manifolds.
Retrieved from the University of Minnesota Digital Conservancy,
https://hdl.handle.net/11299/3811.