Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition

Kunikawa, Keita; Sakurai, Yohei

doi:10.1090/proc/15768

Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition
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by Keita Kunikawa and Yohei Sakurai PDF

Proc. Amer. Math. Soc. 150 (2022), 1767-1777 Request permission

Abstract:

In this paper, on Riemannian manifolds with boundary, we establish a Yau type gradient estimate and Liouville theorem for harmonic functions under Dirichlet boundary condition. Under a similar setting, we also formulate a Souplet-Zhang type gradient estimate and Liouville theorem for ancient solutions to the heat equation.

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