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On the exterior Dirichlet problem for a class of fully nonlinear elliptic equations

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Abstract

In this paper, we mainly establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for a class of fully nonlinear second-order elliptic equations related to the eigenvalues of the Hessian, with prescribed generalized symmetric asymptotic behavior at infinity. Moreover, we give its applications to the Hessian equations, Hessian quotient equations and the special Lagrangian equations, which have been studied previously.

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Acknowledgements

We would like to thank the anonymous referee for his/her carefully reading and helpful comments on the manuscript.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Tangyu Jiang, Haigang Li & Xiaoliang Li

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  1. Tangyu Jiang
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  2. Haigang Li
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  3. Xiaoliang Li
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Correspondence to Xiaoliang Li.

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Communicated by J. Jost.

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H.G. Li was supported by NSFC (11631002, 11971061).

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Jiang, T., Li, H. & Li, X. On the exterior Dirichlet problem for a class of fully nonlinear elliptic equations. Calc. Var. 60, 17 (2021). https://doi.org/10.1007/s00526-020-01904-4

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