## Abstract

In this paper we study the regularity of weak solutions of the elliptic system -div(**A**(*x*,∇**u**)) = **b**(x,∇**u**) with non-standard *ϕ*-growth condition. Here *ϕ* is a given Orlicz function. We are interested in the case where **A** and **b** are not differentiable with respect to *x* but only Hölder continuous with exponent α. We show that the natural quantity **V**(∇**u**) is locally in the Nikolskiĭ space *N*
^{α, 2}. From this it follows that the set of singularities of **V**(∇**u**) has Hausdorff dimension less or equal *n* – 2α, where *n* is the dimension of the domain Ω. One of the main features of our technique is that it handles the case of the *p*-Laplacian for 1 < *p* < ∞ in a unified way. There is no need to use different approaches for the cases *p* ≤ 2 and *p* ≥ 2.

2000 Mathematics Subject Classification: 35J60; 35D10.

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