Question

Dual-mixed formulation for Poisson eq. -- how include Dirichlet BC, since solution only in $L^2$

score 406 · Answer 1 · 2026-03-26 23:09:54

406

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Dual-mixed formulation for Poisson eq. -- how include Dirichlet BC, since solution only in $L^2$

Published on 26 Mar 2026 - 23:09

score 497 · Answer 2 · 2026-03-25 01:22:20

497

Views

Heat equation - Evans

Published on 25 Mar 2026 - 1:22

score 462 · Answer 3 · 2016-04-23 21:45:17

462

Views

Second distributional derivative of cosine

Published on 23 Apr 2016 - 21:45

score 67 · Answer 4 · 2016-04-24 15:25:33

Prove, for an open $\Omega \subset \mathbb{R}^n$ with $x\in \Omega$, that $u\in W^{1,p}(\Omega-\{x\})\implies u\in W^{1,p}(\Omega).$

score 576 · Answer 5 · 2016-04-27 20:11:27

576

Views

Weak Derivative of $x \mapsto \ln(|x|)$ doesn't exists in $(-1,1)$ but in $B_1(0)\in \mathbb{R}^2$

Published on 27 Apr 2016 - 20:11

score 124 · Answer 6 · 2016-04-28 11:09:44

124

Views

Example of a function $u \in W^{1,p}(\Omega)$ whose extension $\hat{u}$ to be $0$ outside $\Omega$ $\hat{u} \notin W^{1,p}(\mathbb{R}^n)$

Published on 28 Apr 2016 - 11:09

score 30 · Answer 7 · 2016-04-28 15:39:31

30

Views

Given $u \in W^{1,p}(\Omega)$ then $\overline{\alpha u} \in W^{1,p}(\Omega)$, with $\alpha \in C^1 \cap L^{\infty},\nabla \alpha \in L^{\infty}$

Published on 28 Apr 2016 - 15:39

score 152 · Answer 8 · 2016-05-04 21:18:09

152

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Question about the proof of $W^{1,p}_0(\Omega) \Rightarrow u=0 $ on $\partial \Omega$

Published on 04 May 2016 - 21:18

score 238 · Answer 9 · 2016-05-05 17:14:12

238

Views

Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$

Published on 05 May 2016 - 17:14

score 385 · Answer 10 · 2016-05-07 12:40:27

385

Views

Passing from Classical Formulation to Weak Forulation on PDEs. Integration by parts in $n$ dimensions?

Published on 07 May 2016 - 12:40

score 247 · Answer 11 · 2016-05-12 14:26:34

247

Views

Weak solutions for elliptic equations

Published on 12 May 2016 - 14:26

score 126 · Answer 12 · 2016-05-13 09:57:03

126

Views

Showing regularity $(u \in C^2(\overline{\Omega}))$ for the Laplacian Problem.

Published on 13 May 2016 - 9:57

score 1.2k · Answer 13 · 2016-05-14 17:34:45

1.2k

Views

Does Green's (first) identity hold for Weak Derivatives?

Published on 14 May 2016 - 17:34

score 338 · Answer 14 · 2016-05-14 22:04:47

338

Views

Confused about the notation $||\nabla u||_{L^p(\Omega)}$

Published on 14 May 2016 - 22:04

score 303 · Answer 15 · 2016-05-16 10:50:54

303

Views

Weak solution in $\mathbb{R}^{N}$

Published on 16 May 2016 - 10:50

List Question

Dual-mixed formulation for Poisson eq. -- how include Dirichlet BC, since solution only in $L^2$

Heat equation - Evans

Second distributional derivative of cosine

Prove, for an open $\Omega \subset \mathbb{R}^n$ with $x\in \Omega$, that $u\in W^{1,p}(\Omega-\{x\})\implies u\in W^{1,p}(\Omega).$

Weak Derivative of $x \mapsto \ln(|x|)$ doesn't exists in $(-1,1)$ but in $B_1(0)\in \mathbb{R}^2$

Example of a function $u \in W^{1,p}(\Omega)$ whose extension $\hat{u}$ to be $0$ outside $\Omega$ $\hat{u} \notin W^{1,p}(\mathbb{R}^n)$

Given $u \in W^{1,p}(\Omega)$ then $\overline{\alpha u} \in W^{1,p}(\Omega)$, with $\alpha \in C^1 \cap L^{\infty},\nabla \alpha \in L^{\infty}$

Question about the proof of $W^{1,p}_0(\Omega) \Rightarrow u=0 $ on $\partial \Omega$

Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$

Passing from Classical Formulation to Weak Forulation on PDEs. Integration by parts in $n$ dimensions?

Weak solutions for elliptic equations

Showing regularity $(u \in C^2(\overline{\Omega}))$ for the Laplacian Problem.

Does Green's (first) identity hold for Weak Derivatives?

Confused about the notation $||\nabla u||_{L^p(\Omega)}$

Weak solution in $\mathbb{R}^{N}$

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