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Motivation for the fractional Sobolev spaces

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#sobolev-spaces #motivation #parabolic-pde #fractional-sobolev-spaces
494
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Is true that $H^{s,p}(\mathbb{R}^n)\subset C^k(\mathbb{R}^n)$ when $s-k>n/p$?.

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#sobolev-spaces #fractional-sobolev-spaces
38
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Is true that $H^{s,p}(\mathbb{R}^n)\subset C^k(\mathbb{R}^n)$ with $s-k>n/p$?.

Published on
#sobolev-spaces #fractional-sobolev-spaces
36
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Immersion $H^s(\Omega) \hookrightarrow H^{s'}(\Omega)$ but with fractional laplacian defined on $\mathbb{R}^N$?

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#integration #integral-inequality #laplacian #fractional-calculus #fractional-sobolev-spaces
110
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Determine if a function is in a fractional Sobolev space

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#real-analysis #functional-analysis #partial-differential-equations #sobolev-spaces #fractional-sobolev-spaces
32
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An extension problem in Sobolev spaces

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#sobolev-spaces #distribution-theory #fractional-sobolev-spaces
130
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Relation between fractional and integer Sobolev norms

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#functional-analysis #inequality #sobolev-spaces #fractional-sobolev-spaces
262
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A trace embedding for fractional Sobolev space

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#functional-analysis #reference-request #sobolev-spaces #fractional-sobolev-spaces #trace-map
129
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Fractional Sobolev norm inverse inequality

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#real-analysis #functional-analysis #inequality #partial-differential-equations #fractional-sobolev-spaces
104
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Complex interpolation between $L^2$ and $H_0^1$

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#functional-analysis #fractional-sobolev-spaces #interpolation-theory
52
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Close an unbounded operator on $H^s(\mathbb{R})$

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#functional-analysis #operator-theory #sobolev-spaces #spectral-theory #fractional-sobolev-spaces
26
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Showing that $ \mathcal{F}^{-1}((1+|\cdot|^2)^{s/2}\mathcal{F}(u))=(Id-\Delta)^{s/2}(u)$

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#sobolev-spaces #fractional-sobolev-spaces
239
Views

Sobolev space $H^s(\mathbb{R}), s<s_0$

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#real-analysis #functional-analysis #hilbert-spaces #sobolev-spaces #fractional-sobolev-spaces
45
Views

Computing the $H^s$ norm of a time-dependent integral operator

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#partial-differential-equations #schwartz-space #fractional-sobolev-spaces
36
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weak-derivative of $u\in H^{3/2}(\Omega)$

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#sobolev-spaces #fractional-sobolev-spaces

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