Inserted: 4 jun 2014
Last Updated: 8 jun 2016
Journal: Nonlinear Anal., Theory Methods Appl.
Links: Link to the published version
We consider a class of vectorial integrals with linear growth, where, as a key feature, some degenerate/singular behavior is allowed. For generalized minimizers of these integrals in BV, we establish interior gradient regularity and --- as a consequence --- uniqueness up to constants. In particular, these results apply, for $1<p<2$, to the singular model integrals \[ \int_\Omega(1+\lvert\nabla w(x)\rvert^p)^\frac1p \,dx\,. \]