Abstract
We extend a theorem of Jörgens, Calabi and Pogorelov on entire solutions of elliptic Monge–Ampère equation to parabolic Monge–Ampère equation, and obtain delicate asymptotic behavior of solutions at infinity. For the dimension \(n\ge 3\), the work of Gutiérrez and Huang in Indiana Univ. Math. J. 47, 1459–1480 (1998) is an easy consequence of our result. And along the line of approach in this paper, we can treat other parabolic Monge–Ampère equations.
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Acknowledgements
All authors are partially supported by NNSF (11371060) and Beijing Municipal Commission of Education for the Supervisor of Excellent Doctoral Dissertation (20131002701). The first author is also supported in part by National natural science foundation of China (11301034) and Deutsche Forschungsgemeinschaft (GRK 1463). They would like to thank Professor YanYan Li for constant encouragement, Professor Elmar Schrohe for helpful discussions and the reviewers for valuable comments.
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Communicated by L. Caffarelli.
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Zhang, W., Bao, J. & Wang, B. An extension of Jörgens–Calabi–Pogorelov theorem to parabolic Monge–Ampère equation. Calc. Var. 57, 90 (2018). https://doi.org/10.1007/s00526-018-1363-5
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DOI: https://doi.org/10.1007/s00526-018-1363-5