Singular solutions of conformal Hessian equation
  We show that for any $\epsilon\in ]0,1[$ there exists an analytic outside zero solution to a uniformly elliptic conformal Hessian equation in a ball $B\subset\R^5$ which belongs to $C^{1,\epsilon} (B)\setminus C^{1,\epsilon+} (B)$. 
Nikolai Nadirashvili, Serge Vladuts
math.AP