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A new local gradient estimate for a nonlinear equation under
integral curvature condition on manifolds
Liang Zhao and Shouwen Fang
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Vol. 306 (2020), No. 2, 755–765
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Abstract
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In this paper, we consider a nonlinear elliptic equation
on complete Riemannian manifolds under integral curvature condition, where
are
two real constants. A new local gradient estimate for positive solutions to this
equation under integral curvature condition is derived, and as an application, we
give a corresponding Harnack inequality.
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Keywords
integral curvature, nonlinear equation, gradient estimate
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Mathematical Subject Classification 2010
Primary: 58J05
Secondary: 58J35
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Milestones
Received: 22 May 2019
Revised: 26 November 2019
Accepted: 2 January 2020
Published: 13 July 2020
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