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arXiv · 2001.01365

Asymptotic behavior at infinity of solutions of Lagrangian mean curvature equations

Jiguang Bao·Zixiao Liu
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Abstract

We studied the asymptotic behavior of solutions with quadratic growth condition of a class of Lagrangian mean curvature equations $F_τ(λ(D^2u))=f(x)$ in exterior domain, where $f$ satisfies a given asymptotic behavior at infinity. When f(x) is a constant near infinity, it is not necessary to demand the quadratic growth condition anymore. These results are a kind of exterior Liouville theorem, and can also be regarded as an extension of theorems of Pogorelov, Flanders and Yuan.

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Jiguang Bao, Zixiao Liu. 2020-01-06. Asymptotic behavior at infinity of solutions of Lagrangian mean curvature equations. https://arxiv.org/abs/2001.01365

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