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 $$...

On page 3 of this preprint, after recalling the definition of flow generated by a vector field, the authors remark that "a necessary condition for a flow $\varphi_t(\cdot)$ generated by $a(t, \cdot)$ ...

Kirszbraun theorem states that if $U$ is a subset of some Hilbert space $H_1$, and $H_2$ is another Hilbert space, and $f : U \to H_2$ is a Lipschitz-continuous map, then $f$ can be extended to a ...

Consider a BV function $u \in BV(\mathbb{R}^N; \mathbb{R}^N)$. What can be said about the difference quotient $$ \frac{u(x+\epsilon y)-u(x)}{\epsilon} $$ regarding its convergence as $\epsilon \to 0$...

Consider the following ODE initial value problem \begin{align*} &\frac{d}{dt}\Phi(t,x) = \boldsymbol{F}(t,\Phi(t,x)), & t \in [0,T], \ \ x \in \mathbb{R}^N,\\ &\Phi(0,x) = x, & x \in \...