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

Abstract

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

21 pages, to appear in Calc. Var. and PDE