完全非线性椭圆方程的非经典解 II：Hessian 方程与八元数
偏微分方程分析
2011-11-03 v3 微分几何
摘要
我们利用八元数代数在 21 维或更高维空间中构造 Hessian 完全非线性一致椭圆方程的奇异解。这些解的正则性是最低可能的。对于 Isaacs 方程也证明了同样的结论。
引用
@article{arxiv.0912.3126,
title = {Nonclassical Solutions of Fully Nonlinear Elliptic Equations II. Hessian Equations and Octonions},
author = {Nikolai Nadirashvili and Serge Vladuts},
journal= {arXiv preprint arXiv:0912.3126},
year = {2011}
}
备注
The 11-dimensional case is moved to arXiv:0805.2694, a section on Isaacs equations is added