Nonclassical Solutions of Fully Nonlinear Elliptic Equations II. Hessian Equations and Octonions
arXiv:0912.3126
Abstract
We use the octonion algebra to construct singular solutions of Hessian fully nonlinear uniformly elliptic equations in 21 or more dimensions. The regularity of these solutions is the least possible one. The same is proven for Isaacs equtions.
The 11-dimensional case is moved to arXiv:0805.2694, a section on Isaacs equations is added