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

Nikolai Nadirashvili; Serge Vladuts

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arXiv · 0912.3126

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

Nikolai Nadirashvili·Serge Vladuts

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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.

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Nikolai Nadirashvili, Serge Vladuts. 2010-03-21. Nonclassical Solutions of Fully Nonlinear Elliptic Equations II. Hessian Equations and Octonions. https://arxiv.org/abs/0912.3126

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