Interior gradient regularity for BV minimizers of singular variational problems

Beck Lisa - Schmidt Thomas

year: 2015
journal: Nonlinear Anal., Theory Methods Appl.
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 \[ \int_\Omega(1+\lvert\nabla w(x)\rvert^p)^\frac1p \,dx\,. \]

The paper is available on the cvgmt preprint server.