Differentiability properties of functions from higher-order Orlicz–Sobolev spaces

We analyze pointwise differentiability properties of functions from (local) Orlicz–Sobolev spaces Wlocm,A(Ω) on an open subset ΩΩ of RnRn, n≥2n≥2. A necessary and sufficient condition on the order of differentiation mm and on the Young function AA is exhibited for any function in Wlocm,A(Ω) to admit a differential of order mm a.e. in ΩΩ. An optimal approximate differentiability property in integral and norm form is established when such a condition fails.