논문KCI 등재
Harnack inequality for parabolic Yamabe-type equation under integral curvature condition on manifolds
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In this paper, we consider Yamabe-type equation $$u_{t}=\triangle u+cu^{\sigma}$$ on complete Riemannian manifolds under integral curvature condition, where $c, \sigma\leq 1 $ are real constants. A new local gradient estimate for positive solutions to this equation is derived and as an application, we give a corresponding Harnack inequality.
Abstract
In this paper, we consider Yamabe-type equation $$u_{t}=\triangle u+cu^{\sigma}$$ on complete Riemannian manifolds under integral curvature condition, where $c, \sigma\leq 1 $ are real constants. A new local gradient estimate for positive solutions to this equation is derived and as an application, we give a corresponding Harnack inequality.
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