Calculus of Variations and Geometric Measure Theory
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L. Beck - T. Schmidt

Interior gradient regularity for $\rm BV$ minimizers of singular variational problems

created by beck on 04 Jun 2014
modified by schmidt on 08 Jun 2016


Published Paper

Inserted: 4 jun 2014
Last Updated: 8 jun 2016

Journal: Nonlinear Anal., Theory Methods Appl.
Volume: 120
Pages: 86-106
Year: 2015
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 \[ \int_\Omega(1+\lvert\nabla w(x)\rvert^p)^\frac1p \,dx\,. \]


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