Local second order regularity of solutions to elliptic Orlicz-Laplace equation

We consider Orlicz-Laplace equation - div ( '(|del|) |del| del ) = where is an Orlicz function and either = 0 or is an element of infinity . We prove local second order regularity results for the weak solutions of the Orlicz-Laplace equation. More precisely, we show that if is another Orlicz function that is close to in a suitable sense, then '(|del|) |del| del is an element of 1,2 loc . This work contributes to the building up of quantitative second order Sobolev regularity for solutions of nonlinear equations.