Question

What would be to show $(1+|\xi|^2)^{s/2}\hat{u}\in \mathcal{S}^{'}(\mathbb R^n)$ is a function?

score 363 · Answer 1 · 2026-04-14 01:43:12

363

Views

What would be to show $(1+|\xi|^2)^{s/2}\hat{u}\in \mathcal{S}^{'}(\mathbb R^n)$ is a function?

Published on 14 Apr 2026 - 1:43

score 182 · Answer 2 · 2026-03-26 14:22:14

182

Views

Bounding $\int_0^T\int_\Omega v|\nabla u|^2$ given that $v \in L^2(0,T;L^2(\Omega))$ and $u \in L^2(0,T;H^1(\Omega)) \cap L^\infty(0,T;L^2(\Omega))$?

Published on 26 Mar 2026 - 14:22

score 391 · Answer 3 · 2026-04-15 15:08:29

391

Views

Is there any Banach space $X$ that $L^2(\Omega)$ is compactly embedded into?

Published on 15 Apr 2026 - 15:08

score 130 · Answer 4 · 2026-04-10 17:14:50

130

Views

Minimizing the homogenuos Sobolev norm for a given trace

Published on 10 Apr 2026 - 17:14

score 97 · Answer 5 · 2026-04-12 06:47:14

97

Views

implications of convergence in sobolev spaces

Published on 12 Apr 2026 - 6:47

score 230 · Answer 6 · 2026-03-26 14:22:19

230

Views

Don't understand proof of a PDE argument, author uses $w(t,\cdot) \in L^6(\Omega)$ when $w(t,\cdot) \in H^1(\Omega)$.

Published on 26 Mar 2026 - 14:22

score 173 · Answer 7 · 2026-03-26 14:21:20

173

Views

A regularity result for a parabolic PDE? Want $u' \in L^\infty((0,T)\times \Omega)$

Published on 26 Mar 2026 - 14:21

score 142 · Answer 8 · 2026-04-13 05:43:49

142

Views

Sobolev Spaces and Convergence

Published on 13 Apr 2026 - 5:43

score 214 · Answer 9 · 2026-04-12 01:28:57

214

Views

On defining appropriate energy. Any principle?

Published on 12 Apr 2026 - 1:28

score 201 · Answer 10 · 2026-04-14 01:12:49

201

Views

About an estimate of theorem 3 in Chapter 12 of Evans' book

Published on 14 Apr 2026 - 1:12

score 319 · Answer 11 · 2026-04-12 00:07:58

319

Views

Closure of partial differential operators on $L^2(\Omega)$

Published on 12 Apr 2026 - 0:07

score 1.9k · Answer 12 · 2026-04-12 03:38:28

1.9k

Views

Compactness of Sobolev Space in L infinity

Published on 12 Apr 2026 - 3:38

score 954 · Answer 13 · 2026-04-13 11:56:37

954

Views

Characterisation of second Sobolev space through Laplacian

Published on 13 Apr 2026 - 11:56

score 395 · Answer 14 · 2026-04-11 14:22:53

395

Views

What is the definition of the Sobolev space $H^1(\Omega)$ with $\Omega=(0,1)\times\mathbb{T}$?

Published on 11 Apr 2026 - 14:22

score 810 · Answer 15 · 2026-04-13 19:19:28

810

Views

Weak convergence for subsequence + pointwise a.e. convergence for the full sequence

Published on 13 Apr 2026 - 19:19

List Question

What would be to show $(1+|\xi|^2)^{s/2}\hat{u}\in \mathcal{S}^{'}(\mathbb R^n)$ is a function?

Bounding $\int_0^T\int_\Omega v|\nabla u|^2$ given that $v \in L^2(0,T;L^2(\Omega))$ and $u \in L^2(0,T;H^1(\Omega)) \cap L^\infty(0,T;L^2(\Omega))$?

Is there any Banach space $X$ that $L^2(\Omega)$ is compactly embedded into?

Minimizing the homogenuos Sobolev norm for a given trace

implications of convergence in sobolev spaces

Don't understand proof of a PDE argument, author uses $w(t,\cdot) \in L^6(\Omega)$ when $w(t,\cdot) \in H^1(\Omega)$.

A regularity result for a parabolic PDE? Want $u' \in L^\infty((0,T)\times \Omega)$

Sobolev Spaces and Convergence

On defining appropriate energy. Any principle?

About an estimate of theorem 3 in Chapter 12 of Evans' book

Closure of partial differential operators on $L^2(\Omega)$

Compactness of Sobolev Space in L infinity

Characterisation of second Sobolev space through Laplacian

What is the definition of the Sobolev space $H^1(\Omega)$ with $\Omega=(0,1)\times\mathbb{T}$?

Weak convergence for subsequence + pointwise a.e. convergence for the full sequence

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