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If $f$ is differentiable everywhere, is $f'$ the weak derivative?

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#real-analysis #analysis #distribution-theory #weak-derivatives
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A derivative identity, for any multi-index.

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#functional-analysis #multivariable-calculus #lp-spaces #weak-derivatives
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Weak derivative zero implies constant function

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#functional-analysis #partial-differential-equations #weak-derivatives
378
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Is it a Sobolev function?

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#functional-analysis #partial-differential-equations #partial-derivative #weak-derivatives
796
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Weak star convergence leads to weak convergence of derivative?

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#functional-analysis #weak-convergence #weak-derivatives #bochner-spaces
516
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Sobolev space on union of two open sets

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#functional-analysis #functions #partial-differential-equations #sobolev-spaces #weak-derivatives
92
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dense subspace of $C(0,T)$

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#real-analysis #convergence-divergence #hilbert-spaces #sobolev-spaces #weak-derivatives
299
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Does existence and uniqueness of a classical solution impose uniqueness of weak solutions to a pde?

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#probability-distributions #partial-differential-equations #weak-derivatives
307
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How can I prove that this function doesn't have a second weak derivative?

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#real-analysis #functional-analysis #lebesgue-integral #weak-derivatives
2k
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Weak derivative as an $L^2$ limit of the difference quotient

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#partial-differential-equations #sobolev-spaces #weak-derivatives
265
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Confused about weak derivatives in Evans

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#functional-analysis #partial-differential-equations #weak-derivatives
243
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Weak differentiation and derivatives of test functions

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#weak-derivatives
206
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Weak convergence of determinant

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#partial-differential-equations #determinant #sobolev-spaces #weak-convergence #weak-derivatives
594
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divergence form of the determinant

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#partial-differential-equations #determinant #sobolev-spaces #weak-convergence #weak-derivatives
28
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approximate a weak derivative

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#real-analysis #weak-derivatives

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