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15
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Differentiation under the ingtegral sign for a $W^{1, \infty}$ function

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#functional-analysis #derivatives #sobolev-spaces
74
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Show $\vert \vert u \vert \vert_{H^k(\Omega)} \leq C[\vert \vert u \vert \vert_{L^2(\Omega)} + |u|_{H^k(\Omega)}]$ using Deny and Lions lemma

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#functional-analysis #partial-differential-equations #sobolev-spaces
85
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Some sort of interpolation equation

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#inequality #partial-differential-equations #sobolev-spaces
140
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Sobolev inequality in 1 dimension

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#real-analysis #functional-analysis #partial-differential-equations #sobolev-spaces
51
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First eigenvalue of the problem $-f^{\prime \prime} = \lambda f $ with $f(-1) = f(1) = 0 $

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#ordinary-differential-equations #partial-differential-equations #sobolev-spaces
132
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Morrey's Inequality: Evan's PDE book

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#partial-differential-equations #sobolev-spaces
36
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$W^{1,p}$ Unity ball is precompact in $L^p$

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#functional-analysis #compactness #sobolev-spaces
31
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Commutator estimates between a contraction evolution group and a differential operator

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#sobolev-spaces #estimation #semigroups #differential-operators #self-adjoint-operators
41
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The behavior of $H^m_0$ functions on non-smooth boundary

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#functional-analysis #partial-differential-equations #sobolev-spaces
37
Views

a question about a Sobolev space notation

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#functional-analysis #sobolev-spaces
52
Views

Laplacian of square integrable functions

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#integration #lebesgue-integral #sobolev-spaces #laplacian
52
Views

Derivative of functions of bounded variation

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#functional-analysis #analysis #measure-theory #sobolev-spaces
38
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Compactness of the trace operator, with explicit constant

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#hilbert-spaces #sobolev-spaces #trace #compact-operators #fractional-sobolev-spaces
104
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How to Apply Martingale Convergence Theorem to Standard Gaussian Random Variables?

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#stochastic-processes #random-variables #normal-distribution #sobolev-spaces #martingales
61
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trace-reverse kind of inequality

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#partial-differential-equations #sobolev-spaces

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