All Questions

What are examples of two BV functions $u:\mathbb{R}^2 \to \mathbb{R}$ with singular derivative? More precisely, I'd like to see an example (and a plot using Mathematica or Matlab) of a function $$...

Let $f: \mathbb R^N \to \mathbb R^N$ be a $BV$ function. Suppose that $\mathrm{div} f$ is absolutely continuous with respect to the Lebesgue measure: $\operatorname{div} f \ll \mathcal L^N$. This ...

Why does the approach used to prove Theorem 4.1 in the paper by Le Bris and Lions on Renormalized solutions of some transport equations with partially $W^{1,1}$ velocities and applications not work ...