List questions from sobolev-spaces

Published on 25 Mar 2026 - 8:09

67

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A function space satisfying $ |f(x) -f(y)| \le ||x|^\theta -|y|^\theta| $

Published on 23 Mar 2026 - 10:22

197

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uniform bound of gradient

Published on 26 Mar 2026 - 2:41

85

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Sobolev spaces and weak derivatives. Meaning of $D^2$

Published on 25 Mar 2026 - 9:53

56

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An integral inequality using duality

Published on 29 Jun 2018 - 9:53

130

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Approximating Sobolev functions on unbounded domains of class $C^1$ by compactly supported smooth functions

Published on 29 Jun 2018 - 12:20

89

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Sequence of subspaces is dense. Limit of Operator norm

Published on 29 Jun 2018 - 12:50

330

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$\theta$-Holder function and weak derivatives

Published on 25 Mar 2026 - 9:53

284

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Definitions of fractional Sobolev Spaces

Published on 23 Mar 2026 - 22:29

434

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Definition of the weak solution to the Dirichlet boundary value problem

Published on 25 Mar 2026 - 3:01

249

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Sobolev spaces on boundary and higher order traces

Published on 25 Mar 2026 - 0:06

54

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Show that the following sequence is unbounded.

Published on 04 Jul 2018 - 9:20

73

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Let $f\in C^\infty(\mathbb T^d)$ satisfy $f\ge0$ and $\hat f(0)=1$. Must $|\hat f(k)|<1$ for all $k\ne0$?

Published on 04 Jul 2018 - 16:56

176

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How can function be assumed smooth in proving Hardy's inequality in Evans book?

Published on 06 Jul 2018 - 9:17

58

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Completing proof of Sobolev embedding theorem

Published on 06 Jul 2018 - 15:38

List Question

Question about characterization of the Sobolev space $W^{1, \infty}(\Omega)$

A function space satisfying $ |f(x) -f(y)| \le ||x|^\theta -|y|^\theta| $

uniform bound of gradient

Sobolev spaces and weak derivatives. Meaning of $D^2$

An integral inequality using duality

Approximating Sobolev functions on unbounded domains of class $C^1$ by compactly supported smooth functions

Sequence of subspaces is dense. Limit of Operator norm

$\theta$-Holder function and weak derivatives

Definitions of fractional Sobolev Spaces

Definition of the weak solution to the Dirichlet boundary value problem

Sobolev spaces on boundary and higher order traces

Show that the following sequence is unbounded.

Let $f\in C^\infty(\mathbb T^d)$ satisfy $f\ge0$ and $\hat f(0)=1$. Must $|\hat f(k)|<1$ for all $k\ne0$?

How can function be assumed smooth in proving Hardy's inequality in Evans book?

Completing proof of Sobolev embedding theorem

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