Abstract
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 ∫Ω(1+|∇w(x)|p)1pdx.
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