All Questions

This question is about some heuristics and graphs of BV functions. In 1-dimensional setting, two key examples of $BV$ functions $u: \mathbb R \to \mathbb R$ are the Heaviside function, whose ...

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 $$...

In this paper, it is written that Alberti’s rank says that the singular part $D^s u$ with respect to $\mathcal L^d$ of the distributional derivative $Du$ of a function $u \in BV_{loc}(\mathbb R^d; \...

Theorem 5.34 in Functions of bounded variation by L. Ambrosio, N. Fusco and D. Pallara states that Let $u \in [BV(\mathbb{R}^N)]^m$. Then there exists a constant $\kappa>0$ such that for every $...

Where can I find a comprehensive survey monograph on functional equations and inequalities from sketch to current research trends with some focus on applications (both inside and outside mathematics)?

I'm very new to the field of numerical analysis of PDE and integro partial differential equations. My advisor (who is not a specialist in this area) highly recommended to read Randall J. LeVeque'...