Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME INTEGRAL INEQUALITIES FOR THE LAPLACIAN WITH DENSITY ON WEIGHTED MANIFOLDS WITH BOUNDARY

  • Fanqi Zeng (School of Mathematics and Statistics Xinyang Normal University)
  • Received : 2022.02.14
  • Accepted : 2022.10.28
  • Published : 2023.03.31
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Abstract

In this paper, we derive a Reilly-type inequality for the Laplacian with density on weighted manifolds with boundary. As its applications, we obtain some new Poincaré-type inequalities not only on weighted manifolds, but more interestingly, also on their boundary. Furthermore, some mean-curvature type inequalities on the boundary are also given.

Keywords

Acknowledgement

This work was supported by NSFC (No.11971415), Natural Science Foundation of Henan (No.212300410235), and the Key Scientific Research Program in Universities of Henan Province (Nos.21A110021, 22A110021) and Nanhu Scholars Program for Young Scholars of XYNU (No.2019).

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