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The Neumann Problem for Hessian Equations

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Abstract

In this paper, we prove the existence of a classical solution to a Neumann boundary value problem for Hessian equations in uniformly convex domain. The method depends upon the establishment of a priori derivative estimates up to second order. So we give an affirmative answer to a conjecture of N. Trudinger in 1987.

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Acknowledgements

Both authors would like to thank the helpful discussion and encouragement from Prof. P. Guan and Prof. X.-J.Wang. The first author would also thank Prof. N. Trudinger and Prof. J. Urbas for their interest and encouragement. The research of the first author was supported by NSFC 11471188 and NSFC 11721101. The second author was supported by the grant from USTC. Both authors were supported by Wu Wen-Tsun Key Lab.

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  1. Guohuan Qiu

    Present address: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, People’s Republic of China

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  1. Department of Mathematics, University of Science and Technology of China, Hefei, People’s Republic of China

    Xinan Ma & Guohuan Qiu

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  1. Xinan Ma
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  2. Guohuan Qiu
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Correspondence to Xinan Ma.

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Communicated by H. T. Yau

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Ma, X., Qiu, G. The Neumann Problem for Hessian Equations. Commun. Math. Phys. 366, 1–28 (2019). https://doi.org/10.1007/s00220-019-03339-1

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