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Obstacle Problems on RCD(K, N) Metric Measure Spaces

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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.

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China

    Sitan Lin

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  1. Sitan Lin
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Correspondence to Sitan Lin.

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Conflict of Interest

The author declares no conflict of interest.

This work was supported by the National Key R&D program of China (2021YFA1003001).

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Lin, S. Obstacle Problems on RCD(K, N) Metric Measure Spaces. Acta Math Sci 43, 1925–1944 (2023). https://doi.org/10.1007/s10473-023-0501-0

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  • DOI: https://doi.org/10.1007/s10473-023-0501-0

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