Question

Why is dirac delta in $H^{-1/2-\epsilon}$ and why is multiplication not well-defined in that space?

score 315 · Answer 1 · 2026-04-14 02:53:35

315

Views

Why is dirac delta in $H^{-1/2-\epsilon}$ and why is multiplication not well-defined in that space?

Published on 14 Apr 2026 - 2:53

score 252 · Answer 2 · 2026-04-12 18:04:38

252

Views

Representation of the Delta function, Riesz dual of evaluation at a point $ev_0: W^{1,2}([-1,1]) \to \mathbb{R}$.

Published on 12 Apr 2026 - 18:04

score 58 · Answer 3 · 2026-04-13 02:35:14

58

Views

Is this sequence bounded in $W_0^{1, p}(\Omega)$?

Published on 13 Apr 2026 - 2:35

score 315 · Answer 4 · 2026-04-12 07:08:42

315

Views

Resolvent of Dirichlet Laplacian via Fourier Transform

Published on 12 Apr 2026 - 7:08

score 156 · Answer 5 · 2026-04-15 19:06:35

156

Views

Weak convergence in $W_0^{1,p}(\Omega)$ implies weak convergence in $(L^2(\Omega))^N$?

Published on 15 Apr 2026 - 19:06

score 45 · Answer 6 · 2026-04-11 08:11:33

45

Views

How to determine the region of integration after switching the order of integration in higher dimensions?

Published on 11 Apr 2026 - 8:11

score 254 · Answer 7 · 2026-04-09 14:49:00

254

Views

How to define real fractional Sobolev space?

Published on 09 Apr 2026 - 14:49

score 85 · Answer 8 · 2026-04-15 11:26:23

85

Views

Inequality for $H^1$-seminorm of a radial function in a ball

Published on 15 Apr 2026 - 11:26

score 284 · Answer 9 · 2026-04-16 02:45:47

284

Views

$u\in H^1(\mathbb{R}^N)\cap C^1 \Rightarrow u$ vanishes at infinity?

Published on 16 Apr 2026 - 2:45

score 322 · Answer 10 · 2026-04-13 15:10:41

322

Views

Fractional Sobolev spaces in 1D and the function $f(x) = x^{\alpha}$

Published on 13 Apr 2026 - 15:10

score 43 · Answer 11 · 2026-04-15 18:28:44

43

Views

Show $\frac{1}{C} \langle t + a_k \rangle \le \langle t+ b_k \rangle \leq C\langle t+ a_k\rangle$

Published on 15 Apr 2026 - 18:28

score 66 · Answer 12 · 2026-04-12 20:36:52

66

Views

Defining Sobolev space of Connections on Determinant Line Bundle

Published on 12 Apr 2026 - 20:36

score 257 · Answer 13 · 2026-04-14 03:38:25

257

Views

Embedding Sobolev space $W^{k,\infty}(U)$ into Hölder space $C^{k-1,\gamma}(U)$

Published on 14 Apr 2026 - 3:38

score 50 · Answer 14 · 2026-04-11 17:50:04

50

Views

Why following trace norm inequality valid?

Published on 11 Apr 2026 - 17:50

score 43 · Answer 15 · 2026-04-14 05:39:19

43

Views

Reference request for trace theorem for $W^{s,p}(\Omega)$ space

Published on 14 Apr 2026 - 5:39

List Question

Why is dirac delta in $H^{-1/2-\epsilon}$ and why is multiplication not well-defined in that space?

Representation of the Delta function, Riesz dual of evaluation at a point $ev_0: W^{1,2}([-1,1]) \to \mathbb{R}$.

Is this sequence bounded in $W_0^{1, p}(\Omega)$?

Resolvent of Dirichlet Laplacian via Fourier Transform

Weak convergence in $W_0^{1,p}(\Omega)$ implies weak convergence in $(L^2(\Omega))^N$?

How to determine the region of integration after switching the order of integration in higher dimensions?

How to define real fractional Sobolev space?

Inequality for $H^1$-seminorm of a radial function in a ball

$u\in H^1(\mathbb{R}^N)\cap C^1 \Rightarrow u$ vanishes at infinity?

Fractional Sobolev spaces in 1D and the function $f(x) = x^{\alpha}$

Show $\frac{1}{C} \langle t + a_k \rangle \le \langle t+ b_k \rangle \leq C\langle t+ a_k\rangle$

Defining Sobolev space of Connections on Determinant Line Bundle

Embedding Sobolev space $W^{k,\infty}(U)$ into Hölder space $C^{k-1,\gamma}(U)$

Why following trace norm inequality valid?

Reference request for trace theorem for $W^{s,p}(\Omega)$ space

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