In this talk, we are going to study a new result for the fractional differentiability of the gradient of solutions to nonlinear elliptic problems. So far, most of the researches on the fractional differentiability estimates have been focused on the fractional differentiability of the gradient of solution which cannot recover the integrability of the solutions. By using the localization argument, we can recover almost every differentiability and integrability of the solutions which can be naturally expected from the problems.