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arXiv:0912.3126 [math.AP]AbstractReferencesReviewsResources

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

Nikolai Nadirashvili, Serge Vladuts

Published 2009-12-16, updated 2010-03-21Version 3

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.

Comments: The 11-dimensional case is moved to arXiv:0805.2694, a section on Isaacs equations is added
Journal: Geom. Func. An. 21 (2011), 483-498
Categories: math.AP, math.DG
Subjects: 35J60
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