Question

If $-\Delta u=f$ in the distributional sense, can we conclude that $\int_Λ(-\Delta u)v\:{\rm d}λ=\int_Λfv\:{\rm d}λ$ for all $v\in H^1(\Lambda)$?

score 119 · Answer 1 · 2016-12-20 22:50:00

119

Views

If $-\Delta u=f$ in the distributional sense, can we conclude that $\int_Λ(-\Delta u)v\:{\rm d}λ=\int_Λfv\:{\rm d}λ$ for all $v\in H^1(\Lambda)$?

Published on 20 Dec 2016 - 22:50

score 100 · Answer 2 · 2016-12-25 17:09:20

100

Views

how to prove that $u\in W^{1,p}(\Omega)$ and $u_k\to u$ weakly in $W^{1,p}(\Omega)$?

Published on 25 Dec 2016 - 17:09

score 74 · Answer 3 · 2016-12-29 23:57:42

74

Views

If $v$ and $w$ are the weak derivatives of $u\in L^p(I,X)$ in $L^q(I,Y)$ and $L^r(I,Z)$ respectively, then $v=w$ almost everywhere

Published on 29 Dec 2016 - 23:57

score 205 · Answer 4 · 2017-01-12 04:51:02

205

Views

Partial Weak Derivatives of multi variable function

Published on 12 Jan 2017 - 4:51

score 181 · Answer 5 · 2017-01-17 15:05:33

181

Views

Weak derivative: recursive definition, or confusing notation?

Published on 17 Jan 2017 - 15:05

score 370 · Answer 6 · 2017-01-19 10:48:08

370

Views

Coincidence of standard derivative and weak derivative

Published on 19 Jan 2017 - 10:48

score 1.2k · Answer 7 · 2017-01-20 16:44:08

1.2k

Views

Piecewise continuously differentiable functions with bounded support have weak derivative

Published on 20 Jan 2017 - 16:44

score 458 · Answer 8 · 2026-03-25 17:52:09

458

Views

Is the weak derivative of any function of the form $f(\lfloor g(x) \rfloor)$ $0$ everywhere?

Published on 25 Mar 2026 - 17:52

score 118 · Answer 9 · 2017-01-26 21:34:55

118

Views

Derivation under the integral sign

Published on 26 Jan 2017 - 21:34

score 54 · Answer 10 · 2026-03-25 10:55:28

54

Views

Regularity of Malgrange-Ehrenpreis solutions

Published on 25 Mar 2026 - 10:55

score 45 · Answer 11 · 2017-02-23 17:04:28

45

Views

How can we prove $\langle(Ψ\cdot∇)Φ,Φ\rangle_{L^2(Λ,\:ℝ^d)}+\frac12\langle(∇\cdotΨ)Φ,Φ\rangle_{L^2(Λ,\:ℝ^d)}=0$ for $Φ,Ψ\in H_0^1(Λ,ℝ^d)$?

Published on 23 Feb 2017 - 17:04

score 427 · Answer 12 · 2017-03-18 05:13:44

427

Views

Weak Gradient of the Unit Ball

Published on 18 Mar 2017 - 5:13

score 158 · Answer 13 · 2017-03-20 16:31:23

158

Views

Integration by substitution for an integral with a gradient

Published on 20 Mar 2017 - 16:31

score 361 · Answer 14 · 2017-03-31 02:54:56

361

Views

Continuity of function in Sobolev W1,1(R^2)

Published on 31 Mar 2017 - 2:54

score 725 · Answer 15 · 2017-03-31 09:36:05

725

Views

How do I show that a distribution is locally p-integrable?

Published on 31 Mar 2017 - 9:36

List Question

If $-\Delta u=f$ in the distributional sense, can we conclude that $\int_Λ(-\Delta u)v\:{\rm d}λ=\int_Λfv\:{\rm d}λ$ for all $v\in H^1(\Lambda)$?

how to prove that $u\in W^{1,p}(\Omega)$ and $u_k\to u$ weakly in $W^{1,p}(\Omega)$?

If $v$ and $w$ are the weak derivatives of $u\in L^p(I,X)$ in $L^q(I,Y)$ and $L^r(I,Z)$ respectively, then $v=w$ almost everywhere

Partial Weak Derivatives of multi variable function

Weak derivative: recursive definition, or confusing notation?

Coincidence of standard derivative and weak derivative

Piecewise continuously differentiable functions with bounded support have weak derivative

Is the weak derivative of any function of the form $f(\lfloor g(x) \rfloor)$ $0$ everywhere?

Derivation under the integral sign

Regularity of Malgrange-Ehrenpreis solutions

How can we prove $\langle(Ψ\cdot∇)Φ,Φ\rangle_{L^2(Λ,\:ℝ^d)}+\frac12\langle(∇\cdotΨ)Φ,Φ\rangle_{L^2(Λ,\:ℝ^d)}=0$ for $Φ,Ψ\in H_0^1(Λ,ℝ^d)$?

Weak Gradient of the Unit Ball

Integration by substitution for an integral with a gradient

Continuity of function in Sobolev W1,1(R^2)

How do I show that a distribution is locally p-integrable?

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