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15
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Showing that a function is a weak time derivative of a Bochner function

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#functional-analysis #partial-differential-equations #lp-spaces #weak-derivatives #bochner-spaces
35
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Weak derivative of function with values in $\mathbb{C}$

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#functional-analysis #derivatives #partial-differential-equations #distribution-theory #weak-derivatives
104
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Composition of differentiable with weakly differentiable function

Published on
#functional-analysis #derivatives #chain-rule #weak-derivatives
35
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Translation of weak solution again a weak solution?

Published on
#partial-differential-equations #weak-derivatives
94
Views

what does it mean: $L^1_{loc}(U)$

Published on
#integration #general-topology #partial-differential-equations #weak-derivatives
38
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Scaling of weak solution to the heat equation

Published on
#partial-differential-equations #weak-derivatives
65
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Compute the second weak derivative of $f(x) = log(x) \: \text{ for } x\in (0,1), f(x) = 0 \: \text{ for }x \in (-1,0)$

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#logarithms #distribution-theory #weak-derivatives
38
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A simple proof of the gradient of the positive part

Published on
#functional-analysis #sobolev-spaces #weak-derivatives
40
Views

Usual derivative vs distributional/discrete derivative for convexity

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#real-analysis #derivatives #continuity #convex-analysis #weak-derivatives
44
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Positiveness of weak solutions of a parabolic PDE

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#real-analysis #functional-analysis #partial-differential-equations #weak-derivatives #parabolic-pde
52
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Constant Higher-order derivatives

Published on
#ordinary-differential-equations #functions #derivatives #weak-derivatives #constants
71
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Weak derivative for $\mathrm{L}^p$-functions

Published on
#sobolev-spaces #distribution-theory #weak-derivatives
140
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Weak continuity in time for a solution to the continuity equation

Published on
#functional-analysis #partial-differential-equations #sobolev-spaces #fluid-dynamics #weak-derivatives
78
Views

Regularity of solutions of one kind of elliptic PDE

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #weak-derivatives
94
Views

Determine whether a function belongs to sobolev space or not.

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#real-analysis #functional-analysis #sobolev-spaces #weak-derivatives

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