Nonclassical Solutions of Fully Nonlinear Elliptic Equations II. Hessian Equations and Octonions

Details Nonclassical Solutions of Fully Nonlinear Elliptic Equations II. Hessian Equations and Octonions Nonclassical Solutions of Fully Nonlinear Elliptic Equations II. Hessian Equations and Octonions

2009-12-16

arxiv.org/abs/0912.3126v3

Geom. Func. An. 21 (2011), 483-498

Mathematics

Analysis of PDEs

The 11-dimensional case is moved to arXiv:0805.2694, a section on Isaacs equations is added

Scientific paper

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.

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