论文标题
外部域上Hessian商方程的DIRICHLET问题
The Dirichlet problem for Hessian quotient equations on exterior domains
论文作者
论文摘要
在本文中，我们考虑了带有右手$ g $的Hessian商方方程的外部Dirichlet问题，其中$ g $是一个正函数，$ g = 1+o（| x | x |^{ - β}）$附近无限，一些$β> 2 $。在无穷大的规定的广义对称渐近行为下，我们通过使用比较原理和Perron的方法建立了粘度溶液的存在和唯一定理。这扩展了Monge和Ampère方程和Hessian方程的先前结果。
In this paper, we consider the exterior Dirichlet problem for Hessian quotient equations with the right hand side $g$, where $g$ is a positive function and $g=1+O(|x|^{-β})$ near infinity, for some $β>2$. Under a prescribed generalized symmetric asymptotic behavior at infinity, we establish an existence and uniqueness theorem for viscosity solutions, by using comparison principles and Perron's method. This extends the previous results for Monge--Ampère equations and Hessian equations.
