On the singular set of BV minimizers for non-autonomous functionals

We investigate regularity properties of minimizers for non-autonomous convex variational integrands [Formula: see text] with linear growth, defined on bounded Lipschitz domains [Formula: see text]. Assuming appropriate ellipticity conditions and Hölder continuity of [Formula: see text] with respect to the first variable, we establish higher integrability of the gradient of minimizers and provide bounds on the Hausdorff dimension of the singular set of minimizers.