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On the second boundary value problem for Lagrangian mean curvature equation

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Abstract

Considering the second boundary value problem of the Lagrangian mean curvature equation, we obtain the existence and uniqueness of the smooth uniformly convex solution, which generalizes the Brendle–Warren’s theorem about minimal Lagrangian diffeomorphism in Euclidean metric space.

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Acknowledgements

The authors would like to express deep gratitude to Prof. Yuanlong Xin for his suggestions and constant encouragement and they are grateful to Prof. Jingyi Chen and Dr.Wei Zhang for their ideas in the special case of \(\tau =\pi /2\) to prove Proposition 1.1. The authors would also like to thank the referees for the helpful suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China

    Chong Wang & Jiguang Bao

  2. Fengtai School of the High School Affiliated to Renmin University of China, Beijing, 100074, China

    Chong Wang

  3. School of Mathematics and Statistics, Guangxi Normal University, Guilin, 541004, Guangxi, China

    Rongli Huang

Authors
  1. Chong Wang
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  2. Rongli Huang
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  3. Jiguang Bao
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Correspondence to Rongli Huang.

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Communicated by A. Mondino.

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Rongli Huang is supported by the National Natural Science Foundation of China (Nos. 11771103 and 11871102) and Guangxi Natural Science Foundation (2017GXNSFFA198017). Jiguang Bao is supported by the National Key Research and Development Program of China (No. 2020YFA0712900) and the National Natural Science Foundation of China (No. 11871102).

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Wang, C., Huang, R. & Bao, J. On the second boundary value problem for Lagrangian mean curvature equation. Calc. Var. 62, 74 (2023). https://doi.org/10.1007/s00526-022-02412-3

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  • DOI: https://doi.org/10.1007/s00526-022-02412-3

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