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If $u(x) = T(u)(x)$ on a subset and $T$ is Lipschitz is $u(x) = T(T(u))(x)$?

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#functional-analysis #sobolev-spaces
70
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Poincaré-type inequality from an article

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#integration #sobolev-spaces
108
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Sobolev embeddings: counter example

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#sobolev-spaces
5.3k
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Proving Poincare in One Dimension

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#inequality #sobolev-spaces
520
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What element of $H^{1/2}$ is the delta function not defined on?

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#sobolev-spaces #dirac-delta
54
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Differential equation en $H^{1}(\Pi)$

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#functional-analysis #analysis #fourier-analysis #hilbert-spaces #sobolev-spaces
124
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If $u \in H^2_0$ and $v \in H^1_0$

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#sobolev-spaces
1.5k
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Bound semi H2 norm by Laplacian

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes
249
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Hilbert Sobolev Spaces

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#functional-analysis #sobolev-spaces
335
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Continuous embedding of magnetic Sobolev space into regular Sobolev space

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#sobolev-spaces #estimation
74
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Inequality of Schmidt: $\int_S |x-y|^{-s} dy \leq \omega_n (n-s)^{-1} R^{n-s},$ where $|S| = e_n R^n = | B_R(x) |$ and $e_n = \frac{\omega_n}{n}$

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#inequality #lebesgue-integral #sobolev-spaces #geometric-measure-theory #decreasing-rearrangements
99
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Limit of the derivative of a sequence on Sobolev space and Norm Question

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#functional-analysis #limits #normed-spaces #sobolev-spaces
110
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Increasing sequence of functions with subsequence that converges in $H^1$ and $L^2$; does the full sequence converge?

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#functional-analysis #sobolev-spaces #monotone-functions
1.1k
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understanding proof of global approximation theorem Evans PDE

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#partial-differential-equations #sobolev-spaces
725
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A $H^{-1}$ norm of a $L^2$ function

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#calculus #real-analysis #functional-analysis #normed-spaces #sobolev-spaces

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