Question

Is $\Vert\cdot\Vert_{L^2}$ Fréchet differentiable as a function on the Sobolev Space $H^1(\mathbb{R})$?

score 65 · Answer 1 · 2026-04-12 04:55:13

65

Views

Is $\Vert\cdot\Vert_{L^2}$ Fréchet differentiable as a function on the Sobolev Space $H^1(\mathbb{R})$?

Published on 12 Apr 2026 - 4:55

score 42 · Answer 2 · 2026-04-10 02:30:12

42

Views

Existence of convergent subsequence in $H^{k}$

Published on 10 Apr 2026 - 2:30

score 115 · Answer 3 · 2026-04-15 16:14:16

115

Views

A ball with slit at the radius is not $W^{1,1}$-extension domain

Published on 15 Apr 2026 - 16:14

score 338 · Answer 4 · 2026-04-17 12:38:38

338

Views

Understanding the space $D^{1,2}(\mathbb{R}^N)$

Published on 17 Apr 2026 - 12:38

score 202 · Answer 5 · 2026-04-12 04:57:37

202

Views

$L^\infty$ norm bounded by $L^2$ norm of certain derivatives

Published on 12 Apr 2026 - 4:57

score 47 · Answer 6 · 2026-04-15 18:57:22

47

Views

Find the elements of the Sobolev space $W^{1,2}$[0, 1] corresponding to the functional on the same space

Published on 15 Apr 2026 - 18:57

score 427 · Answer 7 · 2026-04-15 12:26:17

427

Views

Is $C_c^\infty$ dense in $W^{1,p}\cap C_0$?

Published on 15 Apr 2026 - 12:26

score 273 · Answer 8 · 2026-04-11 16:24:26

273

Views

Chain rule for weak derivatives for composing a Sobolev function with a differentiable function

Published on 11 Apr 2026 - 16:24

score 69 · Answer 9 · 2026-04-10 18:31:56

69

Views

function with summable derivative is uniformly continuous?

Published on 10 Apr 2026 - 18:31

score 50 · Answer 10 · 2026-04-13 22:45:55

50

Views

Whn a Weighted Sobolev space is Hilbert?

Published on 13 Apr 2026 - 22:45

score 99 · Answer 11 · 2026-04-15 00:59:52

99

Views

Kernel generalized divergence convergence

Published on 15 Apr 2026 - 0:59

score 97 · Answer 12 · 2026-04-15 13:03:07

97

Views

If a function $u \in L^p$ in a Lebesgue space has a weak derivative, in what Lebesgue space is the weak derivative?

Published on 15 Apr 2026 - 13:03

score 166 · Answer 13 · 2026-04-11 17:37:18

166

Views

An interpolation argument about homogeneous Sobolev spaces

Published on 11 Apr 2026 - 17:37

score 83 · Answer 14 · 2026-04-14 08:36:00

83

Views

Sobolev space $H^1(\Omega)$ vs homogeneous Sobolev/Beppo-Levi space $\dot{H}^1(\Omega)$

Published on 14 Apr 2026 - 8:36

score 82 · Answer 15 · 2026-04-13 21:14:44

82

Views

A property for functions that belong to the fractional Sobolev space $W^{s,p}\left(\mathbb{R}\right)$

Published on 13 Apr 2026 - 21:14

List Question

Is $\Vert\cdot\Vert_{L^2}$ Fréchet differentiable as a function on the Sobolev Space $H^1(\mathbb{R})$?

Existence of convergent subsequence in $H^{k}$

A ball with slit at the radius is not $W^{1,1}$-extension domain

Understanding the space $D^{1,2}(\mathbb{R}^N)$

$L^\infty$ norm bounded by $L^2$ norm of certain derivatives

Find the elements of the Sobolev space $W^{1,2}$[0, 1] corresponding to the functional on the same space

Is $C_c^\infty$ dense in $W^{1,p}\cap C_0$?

Chain rule for weak derivatives for composing a Sobolev function with a differentiable function

function with summable derivative is uniformly continuous?

Whn a Weighted Sobolev space is Hilbert?

Kernel generalized divergence convergence

If a function $u \in L^p$ in a Lebesgue space has a weak derivative, in what Lebesgue space is the weak derivative?

An interpolation argument about homogeneous Sobolev spaces

Sobolev space $H^1(\Omega)$ vs homogeneous Sobolev/Beppo-Levi space $\dot{H}^1(\Omega)$

A property for functions that belong to the fractional Sobolev space $W^{s,p}\left(\mathbb{R}\right)$

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