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Compact embedding in the the Sobolev space with the Homander vector fields under Carnot-Caretheodary distance

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#functional-analysis #analysis #multivariable-calculus #partial-differential-equations #sobolev-spaces
61
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A sufficient condition to obtain a function with zero average

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#functional-analysis #partial-differential-equations #sobolev-spaces
197
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Converse of the Sobolev Theorem (Exercise 33. from Folland)

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#fourier-analysis #sobolev-spaces #distribution-theory
168
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Laplace operator on $H^{-1}$

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#partial-differential-equations #reference-request #sobolev-spaces #regularity-theory-of-pdes
305
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Geometric implication of the Sobolev embedding

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#functional-analysis #partial-differential-equations #sobolev-spaces #geometric-functional-analysis
81
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Relation between norms

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#functional-analysis #partial-differential-equations #sobolev-spaces
231
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Equaivalent norm on Sobolev space

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#analysis #multivariable-calculus #partial-differential-equations #sobolev-spaces #fractional-sobolev-spaces
110
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Can I extend a weak derivative to the whole $\mathbb R$?

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#lebesgue-integral #lebesgue-measure #sobolev-spaces #weak-derivatives
115
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Sum of norms over elements is not equal to norm over the whole $\Omega$

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#numerical-methods #sobolev-spaces #finite-element-method #interpolation-theory
138
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Is Nehari manifold a topological manifold?

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#partial-differential-equations #manifolds #sobolev-spaces #elliptic-operators
138
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Sobolev space of maps with higher dimensional target?

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#hilbert-spaces #banach-spaces #sobolev-spaces #weak-derivatives
60
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Unfirom convexity of the Sobolev space in the subelliptic case

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#functional-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes
146
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Gradient inequality lower semicontinuity

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#hilbert-spaces #lebesgue-integral #normed-spaces #sobolev-spaces
145
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Why is a null sequence in $L^p(M)$ also a null sequence in $\mathscr{C}^p_k(M)$?

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#riemannian-geometry #smooth-manifolds #sobolev-spaces
243
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Composition of a bounded Lipschitz continuous function with a Sobolev function

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#functional-analysis #sobolev-spaces #lipschitz-functions

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