## 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.## References

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## Additional Information

**Keita Kunikawa**- Affiliation: Cooperative Faculty of Education, Utsunomiya University, 350 Mine-Machi, Utsunomiya 321-8505, Japan
- MR Author ID: 1125978
- ORCID: 0000-0002-5847-9101
- Email: kunikawa@cc.utsunomiya-u.ac.jp
**Yohei Sakurai**- Affiliation: Department of Mathematics, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama-City, Saitama 338-8570, Japan
- MR Author ID: 1205408
- Email: ysakurai@rimath.saitama-u.ac.jp
- Received by editor(s): February 1, 2021
- Received by editor(s) in revised form: July 27, 2021
- Published electronically: January 20, 2022
- Additional Notes: The first author was supported by JSPS KAKENHI (JP19K14521). The second author was supported by JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design” (17H06460).
- Communicated by: Guofang Wei
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**150**(2022), 1767-1777 - MSC (2020): Primary 53C20; Secondary 31C05, 35K05, 35B40, 58J35
- DOI: https://doi.org/10.1090/proc/15768
- MathSciNet review: 4375763