Partial regularity for manifold constrained p(x)-harmonic maps

We prove that manifold constrained $p(x)$-harmonic maps are $C^{1,\beta }$-regular outside a set of zero $n$-dimensional Lebesgue’s measure, for some $\beta \in (0,1)$. We also provide an estimate from above of the Hausdorff dimension of the singular set.