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15
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How to prove that normed space is complete?

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#normed-spaces #lebesgue-measure #banach-spaces #lp-spaces #sobolev-spaces
141
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Examples of open and bounded sets in $\mathbb{R}^d$ satisfying the uniform cone condition

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#general-topology #functional-analysis #sobolev-spaces
119
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Exercise 8.19 - lower semicontinuous - l.s.c - Brezis

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#ordinary-differential-equations #sobolev-spaces
39
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How to deduce from these inequalities that $x_n\to 0$ in $W_0^{1, p}(\Omega)$?

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#real-analysis #calculus #sequences-and-series #inequality #sobolev-spaces
161
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Equivalent definitions of Sobolev space on manifold and references

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#manifolds #riemannian-geometry #smooth-manifolds #lp-spaces #sobolev-spaces
151
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Mean value theorem in Sobolev spaces

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#real-analysis #partial-differential-equations #sobolev-spaces
29
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Sobolev embedding implies lowerbound on the volumn of the ball

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#differential-geometry #riemannian-geometry #sobolev-spaces
341
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Lax-Milgran theorem with the Poisson equation

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#integration #sobolev-spaces #boundary-value-problem #poissons-equation
52
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Bessel inequality for $H^1$ function

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#real-analysis #functional-analysis #sobolev-spaces
143
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Function in $H^1(\mathbb{R})$

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#functional-analysis #hilbert-spaces #sobolev-spaces #fourier-transform #fractional-sobolev-spaces
77
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How to bound non-linear terms of integral operator in Sobolev Space

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#functional-analysis #sobolev-spaces #frechet-derivative
527
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Relationship between Sobolev-Slobodeckij spaces and Besov spaces

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#real-analysis #functional-analysis #partial-differential-equations #sobolev-spaces #fractional-sobolev-spaces
58
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What is the relationship between weak derivatives and the decay of the coefficients in the eigenfunction expansion?

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#sobolev-spaces
111
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Is it possible to find the maximum of $r\ln\left(\ln\left(1+\frac{1}{r}\right)\right)$ for $r\in(0,1)$?

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#real-analysis #calculus #sobolev-spaces
73
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Sobolev inequality for cubes

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#functional-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #fractional-sobolev-spaces

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