Question

$u$ continuous and the weak derivative $Du$ continuous $\Rightarrow$ $u \in C^1$?

score 1k · Answer 1 · 2016-05-16 15:37:36

1k

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$u$ continuous and the weak derivative $Du$ continuous $\Rightarrow$ $u \in C^1$?

Published on 16 May 2016 - 15:37

score 558 · Answer 2 · 2026-03-27 21:56:59

558

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Weak formulation 1-D PDE with non-homogenous robin boundary condition

Published on 27 Mar 2026 - 21:56

score 415 · Answer 3 · 2026-03-27 14:03:35

415

Views

Concerning the proof of regularity of the weak solution for the laplacian problem given in Brezis

Published on 27 Mar 2026 - 14:03

score 79 · Answer 4 · 2016-06-03 15:35:12

79

Views

If $\{\nabla u_j\}$ is Cauchy in $L^p(\mathbb{R}^n)$ and $\int_{B(0,1)} u_j dx = 0$, does $\{u_j\}$ converge in $L^p_{\text{loc}}(\mathbb{R}^n)$?

Published on 03 Jun 2016 - 15:35

score 175 · Answer 5 · 2016-06-07 22:41:10

175

Views

Question concerning the proof of regularity for the Laplacian $f \in H^m(\Omega) \Rightarrow u \in H^{m+2}(\Omega) $

Published on 07 Jun 2016 - 22:41

score 550 · Answer 6 · 2016-06-11 21:52:25

550

Views

Are weak (Sobolev) solutions to a linear ODE a classical ones?

Published on 11 Jun 2016 - 21:52

score 976 · Answer 7 · 2016-06-13 08:41:15

976

Views

Distributional derivatives for functions that is continuous but nowhere differentiable

Published on 13 Jun 2016 - 8:41

score 1.6k · Answer 8 · 2016-06-14 13:30:56

1.6k

Views

Does existence of the second weak derivative of $f\in L^2$ imply existence of the first?

Published on 14 Jun 2016 - 13:30

score 237 · Answer 9 · 2016-06-14 17:49:14

237

Views

Passing from classical formulation to weak formulation for a general PDE

Published on 14 Jun 2016 - 17:49

score 920 · Answer 10 · 2016-06-16 15:12:03

920

Views

Different approaches to differentiability in $L^2$

Published on 16 Jun 2016 - 15:12

score 548 · Answer 11 · 2016-06-18 18:17:34

548

Views

Questions about the proof: Continuous function with weak derivatives $\Rightarrow$ $C^1$

Published on 18 Jun 2016 - 18:17

score 92 · Answer 12 · 2016-06-26 17:10:42

92

Views

How can we extend $\operatorname{div}:C_c^\infty(\Omega)^d\to L^p(\Omega)$ to $W_0^{1,\:p}(\Omega)^d$?

Published on 26 Jun 2016 - 17:10

score 255 · Answer 13 · 2016-06-27 17:10:14

255

Views

If $p$ is a distribution, what is the meaning of the claim $\nabla p\in L^p(\Omega)^d$

Published on 27 Jun 2016 - 17:10

score 260 · Answer 14 · 2016-06-28 11:30:22

260

Views

Proof of the Helmholtz-Hodge decomposition

Published on 28 Jun 2016 - 11:30

score 42 · Answer 15 · 2016-07-02 11:09:01

42

Views

If $p$ is a distribution such that $\nabla p$ is regular, then $p$ must be regular too

Published on 02 Jul 2016 - 11:09

List Question

$u$ continuous and the weak derivative $Du$ continuous $\Rightarrow$ $u \in C^1$?

Weak formulation 1-D PDE with non-homogenous robin boundary condition

Concerning the proof of regularity of the weak solution for the laplacian problem given in Brezis

If $\{\nabla u_j\}$ is Cauchy in $L^p(\mathbb{R}^n)$ and $\int_{B(0,1)} u_j dx = 0$, does $\{u_j\}$ converge in $L^p_{\text{loc}}(\mathbb{R}^n)$?

Question concerning the proof of regularity for the Laplacian $f \in H^m(\Omega) \Rightarrow u \in H^{m+2}(\Omega) $

Are weak (Sobolev) solutions to a linear ODE a classical ones?

Distributional derivatives for functions that is continuous but nowhere differentiable

Does existence of the second weak derivative of $f\in L^2$ imply existence of the first?

Passing from classical formulation to weak formulation for a general PDE

Different approaches to differentiability in $L^2$

Questions about the proof: Continuous function with weak derivatives $\Rightarrow$ $C^1$

How can we extend $\operatorname{div}:C_c^\infty(\Omega)^d\to L^p(\Omega)$ to $W_0^{1,\:p}(\Omega)^d$?

If $p$ is a distribution, what is the meaning of the claim $\nabla p\in L^p(\Omega)^d$

Proof of the Helmholtz-Hodge decomposition

If $p$ is a distribution such that $\nabla p$ is regular, then $p$ must be regular too

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