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      Difference between weak and distributional derivatives

      Aug 1, 2021 · From what I understood, the integral of ($\int_{\Omega} u \varphi dx$) defines a distribution so the distributional derivative is defined as seen in equation above. I understand that while working with weak derivatives, I'm differentiating functions and when one is working with distributional derivatives it's obviously differentiating ...

      distribution theory - Distributional derivative of measures and …

      Mar 17, 2021 · In particular, if f is differentiable, the distributional derivatives is the same as the standard derivative. Now similarly, if $\mu$ is a measure, I think its distributional derivative is defined as the measure $\nu$ such that $\int \phi'd\mu = -\int \phi d\nu$.

      Distributional Partial derivative - Mathematics Stack Exchange

      Sep 23, 2024 · Distributional Derivative of Heaviside Function times Log. 4. What is the intuition behind distributional ...

      analysis - distributional derivative - Mathematics Stack Exchange

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      calculus - Distributional derivative of Weierstrass function ...

      Apr 6, 2019 · Prove that the distributional derivative of the Cantor function is the the $\log_3 2$-Hausdorff measure restricted to the Cantor set 3 When is the distributional derivative a function?

      Find the second distributional derivative of $\\left|\\sin(x)\\right|$

      $\begingroup$ Do you know the chain rule for distributional derivative and the derivative of absolute value map as a distribution? $\endgroup$ – Dr. Tony Tony Chopper Commented May 14, 2023 at 21:08

      functional analysis - How to solve distributional equations ...

      Apr 4, 2019 · Solve the following distributional differential equation: $(xT_f)' \equiv H$ 12 Derivative of principal value distribution $1/x$ is equal to finite part distribution $-1/x^2$?

      distribution theory - When is the distributional derivative a function ...

      Apr 21, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

      functional analysis - Distributional limit. - Mathematics Stack …

      So, the distributional limit is the classical limit $$\lim_{t\to 0}\cos(t\sqrt x)=1$$ ...

      ordinary differential equations - Distributional and weak solutions ...

      Dec 10, 2020 · Solve the following distributional differential equation: $(xT_f)' \equiv H$ 4 Conservation Laws: Difference and Reasonability Weak solutions, Integral solutions, distributional solutions