Harnack inequality for nondivergent elliptic operators on Riemannian manifolds

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Abstract

We consider second-order linear elliptic operators of nondivergence type which are 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 the Harnack inequality of Yau for positive harmonic functions on Riemannian manifolds with nonnegative Ricci curvature using the nondivergence structure of the Laplace operator.

Original languageEnglish
Pages (from-to)281-293
Number of pages13
JournalPacific Journal of Mathematics
Volume213
Issue number2
DOIs
Publication statusPublished - 2004 Feb

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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