  This paper addresses the gain of global fractional regularity in Nikolskii
spaces for solutions of a class of quasilinear degenerate equations with
$(p,q)$-growth. Indeed, we investigate the effects of the datum on the
derivatives of order greater than one of the solutions of the $(p,q)$-Laplacian
operator, under Dirichlet's boundary conditions. As it turns out, even in the
absence of the so-called Lavrentiev phenomenon and without variations on the
order of ellipticity of the equations, the fractional regularity of these
solutions ramifies depending on the interplay between the growth parameters
$p$, $q$ and the data. Indeed, we are going to exploit the absence of this
phenomenon in order to prove the validity up to the boundary of some regularity
results, which are known to hold locally, and as well provide new fractional
regularity for the associated solutions. In turn, there are obtained certain
global regularity results by means of the combination between new a priori
estimates and approximations of the differential operators, whereas the
nonstandard boundary terms are handled by means of a careful choice for the
local frame.
