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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bôcher-type theorem on n-dimensional manifolds with conical metric
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by Jiayu Li and Fangshu Wan PDF
Proc. Amer. Math. Soc. 147 (2019), 4527-4538 Request permission

Abstract:

We generalize the Bôcher-type theorem and give a sharp characterization of the behavior at the isolated singularities of a solution bounded on one side for the equation $\Delta _g u =0$ on singular manifolds with conical metrics. Furthermore, we also obtain a Liouville-type result which demonstrates that the fundamental solution is the unique nontrivial solution of $\operatorname {div}(|x|^\theta \nabla u)=0$ in $\mathbb {R}^n\setminus \{0\}$ that is bounded on one side in both a neighborhood of the origin as well as at infinity.
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Additional Information
  • Jiayu Li
  • Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, AMSS CAS, Beijing 100190, People’s Republic of China
  • MR Author ID: 274510
  • Email: jiayuli@@ustc.edu.cn
  • Fangshu Wan
  • Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, People’s Republic of China
  • MR Author ID: 1179231
  • Email: wfangshu@@mail.ustc.edu.cn
  • Received by editor(s): October 4, 2018
  • Received by editor(s) in revised form: January 20, 2019
  • Published electronically: June 27, 2019
  • Additional Notes: The work was supported by NSFC, No. 11721101.
  • Communicated by: Guofang Wei
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4527-4538
  • MSC (2010): Primary 58J05; Secondary 35J15
  • DOI: https://doi.org/10.1090/proc/14554
  • MathSciNet review: 4002561