Quadratic growth solutions of fully nonlinear elliptic equations with periodic data

Fuente: arXiv
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Main Authors: Li, Dongsheng, Liang, Lichun
Format: Preprint
Published: 2024
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author Li, Dongsheng
Liang, Lichun
author_facet Li, Dongsheng
Liang, Lichun
contents 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-Ampère equations.
format Preprint
id arxiv_https___arxiv_org_abs_2406_13927
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Quadratic growth solutions of fully nonlinear elliptic equations with periodic data
Li, Dongsheng
Liang, Lichun
Analysis of PDEs
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-Ampère equations.
title Quadratic growth solutions of fully nonlinear elliptic equations with periodic data
topic Analysis of PDEs
url https://arxiv.org/abs/2406.13927