数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 1925-1944.doi: 10.1007/s10473-023-0501-0

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OBSTACLE PROBLEMS ON $RCD(K, N)$ METRIC MEASURE SPACES*

Sitan Lin   

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
  • 收稿日期:2022-11-03 修回日期:2023-04-06 出版日期:2023-10-26 发布日期:2023-10-25

OBSTACLE PROBLEMS ON $RCD(K, N)$ METRIC MEASURE SPACES*

Sitan Lin   

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
  • Received:2022-11-03 Revised:2023-04-06 Online:2023-10-26 Published:2023-10-25
  • About author:Sitan Lin, E-mail: linst3@mail3.sysu.edu.cn

摘要: In this paper, we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds. We show the existence and Lipschitz continuity of the solutions, and then we establish some regularities of the free boundaries.

关键词: obstacle problem, metric measure space, Riemannian curvature-dimension condition

Abstract: In this paper, we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds. We show the existence and Lipschitz continuity of the solutions, and then we establish some regularities of the free boundaries.

Key words: obstacle problem, metric measure space, Riemannian curvature-dimension condition

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  • 51K10