Interior gradient regularity for BV minimizers of singular variational problems. (June 2015) - Beck, Lisa; Schmidt, Thomas
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 ) 1 p d x .