# Tagged Questions

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### The $L^2$ convergence of semi-$p$-lapace equation

This question is similar to the one I post early here. But this one might be more reasonable I think... Let $g\in L^\infty(\Omega)$ be given, where $\Omega\subset \mathbb R^2$ is open bounded with ...
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### Does the fundamental theorem of calculus hold for BV functions?

I am a bit confused and I hope you can help me in understanding a bit better these things. Let us start by considering one dimensional case. Let $f\colon \mathbb (a,b) \to \mathbb R$ be a function. ...
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### how can you “fix” one of the definitions of a BV function of one variable?

Math people: My question is similar to that in Two definitions of "Bounded Variation Function" . If you look at that question, you will notice that people treat definitions (1) and (2) ...
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### $\sin(1/x)$ is not BV. [closed]

I have to prove that $$\begin{cases} \begin{array}{cc} \sin(1/x) & x\in \Big(0,\frac{2}{\pi}\Big] \\ 0 & x=0 \end{array} \end{cases}$$ is not of bounded variation. I ...
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### What is the name of this theorem? I do not know how to type some symbols in google.

In my textbook, the following theorem is proved. But I do not understand it. So I am finding some other documents make me understand the theorem. Could someone let me know this theorem's name? Since I ...
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### Pointwise convergence of a sequence of approximate limits of BV functions.

So, let $\Omega\subset \mathbb R^2$ bounded and consider a sequence of functions $\{u_k\}_{k\in\mathbb N}\subset BV(\Omega)$ and $u\in BV(\Omega)$ such that $u_k\rightarrow u$ weakly* in $BV(\Omega)$. ...
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### Can someone prove this bounded variation problem?

I am doing my homework, which is solving all even number problems in textbook. Finally, I have almost finished.... but I failed to solve one problem. I am not sure that it is okay if I post the whole ...
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### Given $f(x) = x^{1/3}$, show that $f \in BV[0, 1]$

I'm learning about functions of bounded variations and need some help with this problem: Given $f(x) = x^{1/3}, x \in [0, 1]$ show that $f \in BV[0, 1]$. My work and thoughts: We know that ...
### Show that $V_{a}^{b}(X_\mathbb{Q}) = +\infty$ on any interval [a, b]
I'm self-studying the theory of functions of bounded variations from the book of Neal Carother (Real Analysis) and need some help with this problem: Show that $V_{a}^{b}(X_\mathbb{Q}) = +\infty$ ...
Let $f$ be a left continuous function of bounded variation on $[a,b]$ s.t. $f(a)=0$. $f$ can be written as the difference $f=f_1-f_2$ of two non-decreasing functions on $[a,b]$. \$f_1=\frac{1}{2}(v(x)...