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We establish pointwise estimates expressed in terms of a nonlinear potential of a generalized Wolff type for A-superharmonic functions with nonlinear operator A : Ω × R n → R n having measurable dependence on the spacial variable and Orlicz growth with respect to the last variable. The result is sharp as the same potential controls bounds from above and from below. Applying it we provide a bunch of precise regularity results including continuity and Hölder continuity for solutions to problems involving measures that satisfies conditions expressed in the natural scales. Finally, we give a variant of Hedberg-Wolff theorem on characterization of the dual of the Orlicz space.

We study the local regularity of vectorial minimizers of integral functionals with standard p-growth. We assume that the non-homogeneous densities are uniformly convex and have a radial structure, with respect to the gradient variable, only at infinity. Under a W1,n-Sobolev dependence on the spatial variable of the integrand, n being the space dimension, we show that the minimizers have the gradient locally in Lq for every q>p. As a consequence, they are locally α-Hölder continuous for every α<1

We prove that local minimizers of the functionalare of class C 0,α for every 0 < α < 1, if the exponent p(x) > 1 has logarithmic modulus of continuity. Moreover, in case the exponent p(x) > 1 is a Hölder continuous function, we establish that minimizers of F (u) are of class C 1,α , for some 0 < α < 1.