SBV compactness theorem
= SBV compactness theorem
{c}
For uniformly bounded values, an $L^p$ <gradient> bound with $p>1$, and bounded $(n-1)$-dimensional jump <measure>, a sequence in the <SBV space> admits an $L^1$-convergent subsequence whose limit remains special. <Gradients> converge weakly in $L^p$, and jump <measure> is <lower semicontinuous>. These hypotheses prevent diffuse singular <derivatives> from replacing the controlled interfaces in a minimizing limit.