BV supersolutions to equations of 1-Laplace and minimal surface type (Q285637)

In the very interesting paper under review, the authors introduce and analyze the notion of BV supersolutions to the Dirichlet problem for the 1-Laplace and the minimal surface equations NEWLINENEWLINE\[NEWLINE \text{div\,}\frac{Du}{|Du|}=0,\quad \text{div\,} \frac{Du}{\sqrt{1+|Du|^2}}=0, NEWLINE\]NEWLINE NEWLINEand also for equations of similar type. Of particular interest are the related compactness and consistency results established.NEWLINENEWLINEThe machinery employed rely on a generalized product of \(L^\infty\) divergence-measure fields and gradient measures of BV functions. That product crucially depends on the choice of a representative of the BV function, and the proofs of its basic properties involve results on one-sided approximation and fine semicontinuity in the BV context.