Harnack inequality for nondivergent elliptic operators on Riemannian manifolds

Research output: Contribution to journalArticle

13 Citations (Scopus)

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 Jan 1

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Harnack Inequality
Elliptic Operator
Riemannian Manifold
Nonnegative Curvature
Ricci Curvature
Sectional Curvature
Laplace Operator
Harmonic Functions
Linear Operator
Non-negative

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Harnack inequality for nondivergent elliptic operators on Riemannian manifolds. / Kim, Seick.

In: Pacific Journal of Mathematics, Vol. 213, No. 2, 01.01.2004, p. 281-293.

Research output: Contribution to journalArticle

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