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

  • Sitan Lin
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  • Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
Sitan Lin, E-mail: linst3@mail3.sysu.edu.cn

Received date: 2022-11-03

  Revised date: 2023-04-06

  Online published: 2023-10-25

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.

Cite this article

Sitan Lin . OBSTACLE PROBLEMS ON $RCD(K, N)$ METRIC MEASURE SPACES*[J]. Acta mathematica scientia, Series B, 2023 , 43(5) : 1925 -1944 . DOI: 10.1007/s10473-023-0501-0

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