Existence of multi-valued solutions with asymptotic behavior of parabolic Monge-Ampère equation

Boundary value problems

Limei Dai¹ 

[1] School of Mathematics and Information Science, Weifang University, Weifang, China

关键词: parabolic Monge-Ampère equation;    multi-valued solutions;    asymptotic behavior;    Perron method;    35K96;    35B40;   

DOI  :  10.1186/s13661-015-0307-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we extend the results of multi-valued solutions of elliptic Monge-Ampère equation to parabolic Monge-Ampère equation. We use the Perron method to prove the existence of multi-valued solutions with asymptotic behavior at infinity of parabolic Monge-Ampère equation. Moreover, we prove that the multi-valued solution is continuous in the whole space.

【 授权许可】

CC BY