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Existence and uniqueness of weak solutions to the homogeneous biharmonic equation.

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#boundary-value-problem #weak-derivatives #elliptic-operators #variational-analysis
533
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Is the square of an $H^1$ function also $H^1$?

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#sobolev-spaces #lp-spaces #weak-derivatives
136
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Regularity of the Divergence of Weak Solutions to Elliptic PDEs

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#integration #sobolev-spaces #weak-derivatives #elliptic-equations
712
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Recovering classical solution from weak one for the Laplace equation

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#proof-verification #partial-differential-equations #hilbert-spaces #sobolev-spaces #weak-derivatives
65
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Exercise on first and second order derivative in sense of distributions.

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#analysis #weak-derivatives
1k
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Radon-Nikodym derivative of discrete measure

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#proof-verification #lebesgue-measure #weak-derivatives
172
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$\mathbb{1}_{B_1(0)}$ doesn't have a $\partial_{x_i}$weak derivative in $\mathbb{R}^n$

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#partial-differential-equations #sobolev-spaces #weak-derivatives
374
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Ito's formula for merely continuous functions

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#stochastic-calculus #brownian-motion #martingales #weak-derivatives
88
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Sobolev spaces on different domains

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#partial-differential-equations #sobolev-spaces #weak-derivatives
218
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Why the generalized derivatives defined? Why was it needed?

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#derivatives #sobolev-spaces #weak-derivatives
1.9k
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Proving the characteristic function is not weakly differentiable on $\mathbb{R}^n$.

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#functional-analysis #weak-derivatives
173
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A Sobolev map with smooth weak derivative is smooth?

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#real-analysis #multivariable-calculus #sobolev-spaces #weak-derivatives
130
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Are points negligible for weak derivative in dimension 2?

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#real-analysis #functional-analysis #sobolev-spaces #distribution-theory #weak-derivatives
1.2k
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Problem 13 - Chapter 5 - Evans' PDE (Second Edition)

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#partial-differential-equations #sobolev-spaces #lipschitz-functions #weak-derivatives
702
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Sobolev inequality and chain rule

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#sobolev-spaces #lp-spaces #weak-derivatives

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