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arXiv · 2406.13927

Quadratic growth solutions of fully nonlinear elliptic equations with periodic data

Dongsheng Li·Lichun Liang
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Abstract

In this paper, we study quadratic growth solutions $u$ of fully nonlinear elliptic equations of the form $F(D^2u)=f$ in $\mathbb{R}^n$, where $f$ is periodic and $F$ may be not uniformly elliptic. The existence of solutions and Liouville type results in the whole space and exterior domains are established, which generalize the classical results when $f$ is constant. As applications, the corresponding results are given to $k$-Hessian equations, which include the celebrated results for Monge-Amp\`{e}re equations.

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Dongsheng Li, Lichun Liang. 2024-06-20. Quadratic growth solutions of fully nonlinear elliptic equations with periodic data. https://arxiv.org/abs/2406.13927

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