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Existence of a (weak) antiderivative for any given $f \in L^1(\mathbb{R}^n, \mathbb{R}^n)$

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#multivariable-calculus #sobolev-spaces #weak-derivatives
42
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Does the product rule always hold in one dimensions?

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#real-analysis #sobolev-spaces #weak-derivatives #absolute-continuity
52
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Validity of pointwise estimate involving spatial derivative of Sobolev function

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#derivatives #sobolev-spaces #weak-derivatives
77
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Weak derivative different from the classical one.

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#real-analysis #partial-differential-equations #weak-derivatives
82
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Definition of weak directional derivative

Published on
#sobolev-spaces #weak-derivatives
29
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A problem of continuity at an endpoint

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#continuity #sobolev-spaces #weak-derivatives
34
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Density of compactly supported functions in a Sobolev space

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#functional-analysis #derivatives #sobolev-spaces #weak-derivatives
42
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Distributional and classical derivative

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#real-analysis #derivatives #distribution-theory #weak-derivatives
14
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Reverse inequality for Riemann-Liouville fractional integral

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#real-analysis #integration #analysis #derivatives #weak-derivatives
56
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Variational formulation for the heat equation

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#partial-differential-equations #heat-equation #weak-derivatives
59
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Computing the distributional derivative of a particular function

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#calculus #functional-analysis #distribution-theory #weak-derivatives
25
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Fixing a variable of a $H^1_0(\Omega)$ function

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#lebesgue-integral #sobolev-spaces #weak-derivatives
13
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Schwarz rearrangement for a function with one variable fixed

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#lebesgue-integral #sobolev-spaces #weak-derivatives #decreasing-rearrangements
20
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Doubt about Pólya–Szegő inequality

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#sobolev-spaces #weak-derivatives #decreasing-rearrangements
64
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$L^2$-convergence implies convergence in $H_0^k$

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#partial-differential-equations #convergence-divergence #sobolev-spaces #weak-derivatives

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