Local behaviour of the second order derivatives of solutions to $p$-Laplace equations

We consider the equation $-{\mathrm{\Delta }}_{p}u=f(x)$ in $\mathrm{\Omega },$ where ${\mathrm{\Delta }}_p$ is the $p$-Laplace operator. We provide $L^{\mathrm{\infty }}$-type estimates for the second derivatives of solutions when $p$ approaches to $2$.