A note on interior $W^{2,1+\varepsilon}$ estimates for the Monge-Ampere   equation
  By a variant of the techniques introduced by the first two authors in [DF] to prove that second derivatives of solutions to the Monge-Ampere equation are locally in $L\log L$, we obtain interior $W^{2,1+\varepsilon}$ estimates. 
Guido De philippis, Alessio Figalli, Ovidiu Savin
math.AP