数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (6): 2193-2203.doi: 10.1007/s10473-022-0601-2

• 论文 • 上一篇    下一篇

MONOTONICITY FORMULAS FOR PARABOLIC FREE BOUNDARY PROBLEMS ON CONES

Chung-Kwong Chan, Huichun Zhang, Xiping Zhu   

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • 收稿日期:2022-04-07 修回日期:2022-05-09 出版日期:2022-12-25 发布日期:2022-12-16
  • 通讯作者: Huichun ZHANG, E-mail: zhanghc3@mail.sysu.edu.cn E-mail:zhanghc3@mail.sysu.edu.cn
  • 基金资助:
    The second author was partially supported by National Key R&D Program of China (2021YFA1003001) and NSFC 12025109, and the third author was partially supported by NSFC (11521101).

MONOTONICITY FORMULAS FOR PARABOLIC FREE BOUNDARY PROBLEMS ON CONES

Chung-Kwong Chan, Huichun Zhang, Xiping Zhu   

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2022-04-07 Revised:2022-05-09 Online:2022-12-25 Published:2022-12-16
  • Contact: Huichun ZHANG, E-mail: zhanghc3@mail.sysu.edu.cn E-mail:zhanghc3@mail.sysu.edu.cn
  • Supported by:
    The second author was partially supported by National Key R&D Program of China (2021YFA1003001) and NSFC 12025109, and the third author was partially supported by NSFC (11521101).

摘要: Monotonicity formulas play a central role in the study of free boundary problems. In this note, we develop a Weiss-type monotonicity formula for solutions to parabolic free boundary problems on metric measure cones.

关键词: monotonicity formula, parabolic free boundary problem, RCD-spaces

Abstract: Monotonicity formulas play a central role in the study of free boundary problems. In this note, we develop a Weiss-type monotonicity formula for solutions to parabolic free boundary problems on metric measure cones.

Key words: monotonicity formula, parabolic free boundary problem, RCD-spaces

中图分类号: 

  • 51K10