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Properties of Functions in $W^{1,p}(\Omega)$ and Their Weak Derivatives

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#sobolev-spaces #weak-derivatives #almost-everywhere
107
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Showing an integral with respect to some Borel Measure is finite.

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#measure-theory #lebesgue-integral #weak-derivatives #radon-nikodym
67
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What is the average value of $x + \sqrt{2}\, y$ over all integer points in the ellipse $x^2 + 2y^2 < N$?

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#number-theory #continuity #numerical-methods #weak-derivatives
252
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A question about distributions and Lp spaces

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#lp-spaces #distribution-theory #weak-derivatives
126
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Hörmander's proof of: $ u, f \in C(\Omega) $, $ D_j u = f $ in distribution sense $ \implies $ $ D_j u = f $ classically.

Published on
#analysis #uniform-convergence #distribution-theory #convolution #weak-derivatives
827
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Weak and classical derivatives: an overview

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#functional-analysis #lp-spaces #distribution-theory #weak-derivatives
269
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A.e. differentiable weak derivative

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#real-analysis #sobolev-spaces #weak-derivatives
170
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Nonnegativity of solution of $u_t=\Delta u+u$

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#measure-theory #partial-differential-equations #lebesgue-integral #lp-spaces #weak-derivatives
72
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Convolution between a distributional derivative and a measure

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#real-analysis #functional-analysis #convergence-divergence #convolution #weak-derivatives
281
Views

Weak derivative under the integral sign

Published on
#real-analysis #partial-differential-equations #lebesgue-integral #partial-derivative #weak-derivatives
548
Views

Weak differentiability and polar coordinates

Published on
#sobolev-spaces #polar-coordinates #change-of-variable #weak-derivatives
109
Views

Differentiating a Distribution

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#distribution-theory #weak-derivatives
55
Views

Difference between $L^2$ and $L_{\sigma}^{2}$

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#real-analysis #functions #lp-spaces #weak-derivatives #smooth-functions
476
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Existence of higher order weak derivative implies existence of lower order if integrable (1 dim). Proof?

Published on
#functional-analysis #partial-differential-equations #weak-derivatives
301
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What is the Sobolev space of maps between surfaces?

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#manifolds #sobolev-spaces #riemann-surfaces #weak-derivatives

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