发表机构
Chalmers University of Technology and University of Gothenburg（查尔姆斯理工大学和哥德堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究紧致黎曼流形上的一般完全非线性椭圆Hessian方程，通过弱化标准对称性假设，在推导先验估计后利用连续性方法求解。
AI 中文摘要
我们研究紧致黎曼流形上一类一般的完全非线性椭圆Hessian方程。特别地，我们将Caffarelli、Nirenberg和Spruck所提出的标准假设（即方程为Hessian特征值的对称函数）替换为更弱的假设。在对方程施加适当假设并推导出解的先验估计后，我们利用连续性方法求解该方程。
英文摘要
We study a general class of fully non-linear elliptic Hessian equations on compact Riemannian manifolds. In particular, we replace the standard assumption that the equation is a symmetric function of the eigenvalues of the Hessian made by Caffarelli, Nirenberg and Spruck by a weaker one. After deriving a priori estimates for solutions under suitable assumptions on the equation, we solve it with a continuity method.
Comments40 pages, 6 figures, First paper of a series of three
