Non-classical Solution to Hessian Equation from Cartan Isoparametric   Cubic
  We show how to construct a non-smooth solution to Hessian fully nonlinear second-order uniformly elliptic equation using the Cartan isoparametric cubic in 5 dimensions. 
Nikolai Nadirashvili, Vladimir Tkachev, Serge Vladuts
math.AP math.DG