Question

Why $\mathcal C^\infty (\Omega )\cap W^{k,p}(\Omega )$ dense in $W^{k,p}(\Omega )$ instead of $\mathcal C^\infty (\Omega )$.

score 363 · Answer 1 · 2026-04-13 08:40:47

Why $\mathcal C^\infty (\Omega )\cap W^{k,p}(\Omega )$ dense in $W^{k,p}(\Omega )$ instead of $\mathcal C^\infty (\Omega )$.

score 71 · Answer 2 · 2026-04-16 09:55:39

71

Views

Applying Fourier transform to solve a PDE

Published on 16 Apr 2026 - 9:55

score 276 · Answer 3 · 2026-04-15 07:13:40

276

Views

Equivalents norms in Sobolev Spaces ${\bf H}^1_0$ and ${\bf V}$.

Published on 15 Apr 2026 - 7:13

score 1.3k · Answer 4 · 2026-04-12 23:33:18

1.3k

Views

Are the $L^\infty$ functions differentiable?

Published on 12 Apr 2026 - 23:33

score 153 · Answer 5 · 2026-04-09 09:14:50

153

Views

Problem to understand Sobolev imbedding.

Published on 09 Apr 2026 - 9:14

score 297 · Answer 6 · 2026-04-11 17:32:32

297

Views

Weak equation of Euler Lagrange

Published on 11 Apr 2026 - 17:32

score 1k · Answer 7 · 2026-04-14 14:06:03

1k

Views

Density of test functions in Sobolev space in $\mathbb{R}^n \setminus \{ 0 \}$

Published on 14 Apr 2026 - 14:06

score 55 · Answer 8 · 2026-04-10 07:07:32

55

Views

What is $W_{loc}^{2,2}(\Omega )$?

Published on 10 Apr 2026 - 7:07

score 213 · Answer 9 · 2026-03-28 08:27:52

213

Views

What is the weak derivative of $|x|$?

Published on 28 Mar 2026 - 8:27

score 3.5k · Answer 10 · 2026-04-16 14:05:34

3.5k

Views

Norm on the Space $H^{-1}$

Published on 16 Apr 2026 - 14:05

score 32 · Answer 11 · 2026-04-16 17:43:35

32

Views

Why is there a sequence $u_n\in X\cap \mathcal C^2[-1,1]$ s.t. $u_n\to u$ in $W^{1,2}(-1,1)$?

Published on 16 Apr 2026 - 17:43

score 26 · Answer 12 · 2026-04-15 07:31:56

26

Views

If $\Vert f(t,x)\Vert_{W^{1,\infty}((0,\infty)\times \mathbb{R})}\le C$, what conditions imply $f(t,x) \to g(x)$ uniformly as $t \to \infty$?

Published on 15 Apr 2026 - 7:31

score 178 · Answer 13 · 2026-04-11 22:57:22

178

Views

Consistency of Dirac delta representations in $H^{-1}(\mathbb{R})$

Published on 11 Apr 2026 - 22:57

score 332 · Answer 14 · 2026-04-16 10:10:34

332

Views

$H^1_0$ on half space

Published on 16 Apr 2026 - 10:10

score 131 · Answer 15 · 2026-03-28 08:28:02

131

Views

Surjectivity of differential operator between Sobolev spaces

Published on 28 Mar 2026 - 8:28

List Question

Why $\mathcal C^\infty (\Omega )\cap W^{k,p}(\Omega )$ dense in $W^{k,p}(\Omega )$ instead of $\mathcal C^\infty (\Omega )$.

Applying Fourier transform to solve a PDE

Equivalents norms in Sobolev Spaces ${\bf H}^1_0$ and ${\bf V}$.

Are the $L^\infty$ functions differentiable?

Problem to understand Sobolev imbedding.

Weak equation of Euler Lagrange

Density of test functions in Sobolev space in $\mathbb{R}^n \setminus \{ 0 \}$

What is $W_{loc}^{2,2}(\Omega )$?

What is the weak derivative of $|x|$?

Norm on the Space $H^{-1}$

Why is there a sequence $u_n\in X\cap \mathcal C^2[-1,1]$ s.t. $u_n\to u$ in $W^{1,2}(-1,1)$?

If $\Vert f(t,x)\Vert_{W^{1,\infty}((0,\infty)\times \mathbb{R})}\le C$, what conditions imply $f(t,x) \to g(x)$ uniformly as $t \to \infty$?

Consistency of Dirac delta representations in $H^{-1}(\mathbb{R})$

$H^1_0$ on half space

Surjectivity of differential operator between Sobolev spaces

Trending Questions

Popular # Hahtags

Popular Questions