For question about weak derivatives, a notion which extends the classical notion of derivative and allows us to consider derivatives of distributions rather than functions.
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Finding the weak derivative of order $3$ of $f(x)=\operatorname{sgn} \sin(x)$ where $\operatorname{sgn}$ is the sign function
Let $$f(x)=\operatorname{sgn} \sin(x)$$ where $\operatorname{sgn}$ is sign function. I need to find the weak derivative of order 3 for $f(x)$?
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84 views
Weak derivative of $\operatorname{sgn}(x_1)$
Let $x\in \mathbb{R}^{n}, x = (x_1,\ldots,x_n)$, and $f(x) = \operatorname{sgn}(x_{1})$. Is $f$ weakly differentiable on $U = B(0,1)$, i.e. unit ball in $\mathbb{R}^{n}$, and what is the weak ...
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When the weak derivative just is the strong (or classical) derivative?
When the weak derivative just is the strong (or classical) derivative? For instance, can we prove that weak derivate $Du\in C^\alpha$(or $C^0$) implies $u\in C^{1,\alpha}$(or $C^1$).
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A weak chainrule [Urbano, Intrinsic Scaling]
Hey I'm reading the book on intrinsic scalign by Urbano an there is a certain issue i have problems with.
Essentially the problem is the following. Let $\Omega\subset \mathbb{R}^n$ be a bounded ...
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Weak derivative
Let $u \in C(\Omega)$ be a function with weak derivative $Du \in C(\Omega)^n$. How does one prove that $Du$ coincides with the classical derivative?
Is the mean value theorem for integration ...
