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Show that this function is weakly differentiable

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#real-analysis #partial-differential-equations #sobolev-spaces #weak-derivatives
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Continuous function without a weak derivative

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#continuity #weak-derivatives
319
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Dirac Delta function to solve PDE in the sense of distribution

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#partial-differential-equations #dirac-delta #weak-derivatives
94
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Weak derivative of $t^{\beta-1}$

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#analysis #weak-derivatives
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Compact support of derivatives of $u$ in weak sense

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#analysis #sobolev-spaces #weak-derivatives #regularity-theory-of-pdes
233
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Interpolation between derivatives

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#functional-analysis #inequality #lebesgue-integral #sobolev-spaces #weak-derivatives
237
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How to solve a simple differential equation in the way of weak solutions?

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#partial-differential-equations #partial-derivative #weak-derivatives #regularity-theory-of-pdes
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Does convergence in H1 imply pointwise convergence?

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#convergence-divergence #lebesgue-integral #weak-derivatives
484
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Computing weak derivatives on an open square

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#partial-differential-equations #sobolev-spaces #weak-derivatives
307
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Prove that each $W_0^{1,2}$-function is weakly differentiable

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#ordinary-differential-equations #partial-differential-equations #convergence-divergence #sobolev-spaces #weak-derivatives
85
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$L^2$ inner product split over sub-domains in $\mathbb{R}^3$

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#functional-analysis #hilbert-spaces #sobolev-spaces #inner-products #weak-derivatives
463
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Weak convergence in the Sobolev space and compact embeddedness

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#partial-differential-equations #convergence-divergence #sobolev-spaces #weak-convergence #weak-derivatives
129
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Continuously differentiable functions are weakly differentiable

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#ordinary-differential-equations #partial-differential-equations #sobolev-spaces #weak-derivatives
103
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If $\nabla u\in L^2(\mathbb{R}^n)$, then $u\in L^2_{loc}(\mathbb{R}^n)$

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#real-analysis #weak-derivatives
234
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Is the regularity of $u$ necessary to deduce this result? (Evans PDE)

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#sobolev-spaces #weak-convergence #weak-derivatives

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