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On singular Abreu equations in higher dimensions

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Abstract

We study the solvability of the second boundary value problem of a class of highly singular, fully nonlinear fourth order equations of Abreu type in higher dimensions under either a smallness condition or radial symmetry.

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Acknowledgement

The author would like to thank Connor Mooney for critical comments on a previous version of this paper. The author also thanks the anonymous referee for his/her crucial comments and suggestions that helped strengthen and simplify the proof of Theorem 1.3.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, 831 E 3rd St, Bloomington, IN, 47405, USA

    Nam Q. Le

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  1. Nam Q. Le
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Correspondence to Nam Q. Le.

Additional information

The research of the author was supported in part by the National Science Foundation under grant DMS-1764248

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Le, N.Q. On singular Abreu equations in higher dimensions. JAMA 144, 191–205 (2021). https://doi.org/10.1007/s11854-021-0176-1

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  • DOI: https://doi.org/10.1007/s11854-021-0176-1

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