Acta mathematica scientia,Series B ›› 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
  • Received:2022-11-03 Revised:2023-04-06 Published:2023-10-25
  • About author:Sitan Lin, E-mail: linst3@mail3.sysu.edu.cn

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

CLC Number: 

  • 51K10
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