Question

Weak problem formulation for PDE and boundary conditions

score 535 · Answer 1 · 2016-07-16 13:50:58

535

Views

Weak problem formulation for PDE and boundary conditions

Published on 16 Jul 2016 - 13:50

score 358 · Answer 2 · 2016-07-17 10:45:57

358

Views

Understanding the definition of $W_0^{k,p}$

Published on 17 Jul 2016 - 10:45

score 663 · Answer 3 · 2016-07-17 17:04:25

663

Views

Using scaling arguments to determine relationships between Sobolev spaces?

Published on 17 Jul 2016 - 17:04

score 179 · Answer 4 · 2016-07-18 06:50:55

179

Views

Why if $u_h \rightharpoonup u$ in $*w-W^{1,\infty}$ then exists a subsequence s.t. $u_{h_k}\rightarrow u$ in $L^{\infty}$?

Published on 18 Jul 2016 - 6:50

score 141 · Answer 5 · 2026-03-27 22:53:53

141

Views

If $\mathcal H$ is the closure of the set $D$ of divergence-free smooth functions in $L^2$, then $H_0^1∩\mathcal H$ is the closure of $D$ in $H_0^1$

Published on 27 Mar 2026 - 22:53

score 1.6k · Answer 6 · 2026-03-25 11:13:36

1.6k

Views

Different definitions of Besov norm/space

Published on 25 Mar 2026 - 11:13

score 46 · Answer 7 · 2016-07-19 10:06:12

46

Views

How to think of Sobolev spaces $W^{k, p}$ for a function that is no longer an element of $W^{k, p}$ for $p$ greater than some number?

Published on 19 Jul 2016 - 10:06

score 504 · Answer 8 · 2026-03-26 16:06:45

504

Views

$W^{1,1}\subseteq AC$ and a certain property implies BV: why?

Published on 26 Mar 2026 - 16:06

score 54 · Answer 9 · 2016-07-19 16:50:08

54

Views

Does $f \in W^{2,p}(a,b)$ imply $f \in C^1([a,b])$?

Published on 19 Jul 2016 - 16:50

score 52 · Answer 10 · 2026-03-28 14:05:34

52

Views

The eigenvalue of Laplace problem on a domain with a line removed

Published on 28 Mar 2026 - 14:05

score 60 · Answer 11 · 2026-04-02 10:08:24

60

Views

The eigenfunction of modified 1-laplace equation

Published on 02 Apr 2026 - 10:08

score 168 · Answer 12 · 2026-03-27 00:10:10

168

Views

Why is $W^{k,p}(\Omega)$ the completion of $(\widetilde{C}^k(\Omega)$ instead of $W^{k,p}(\Omega) = (\widetilde{C}^k(\Omega)$?

Published on 27 Mar 2026 - 0:10

score 282 · Answer 13 · 2016-07-20 18:34:58

282

Views

Does the validity of Sobolev inequality on a domain imply it's a Sobolev extension domain?

Published on 20 Jul 2016 - 18:34

score 122 · Answer 14 · 2026-03-27 13:25:22

122

Views

I don't see why $W^{1, 2}(\partial D)$ being compactly embedded in $L^2(\partial D)$ lets us show an operator is Fredholm of index zero.

Published on 27 Mar 2026 - 13:25

score 1.3k · Answer 15 · 2026-03-26 12:40:49

1.3k

Views

Weak derivative of maximum

Published on 26 Mar 2026 - 12:40

List Question

Weak problem formulation for PDE and boundary conditions

Understanding the definition of $W_0^{k,p}$

Using scaling arguments to determine relationships between Sobolev spaces?

Why if $u_h \rightharpoonup u$ in $*w-W^{1,\infty}$ then exists a subsequence s.t. $u_{h_k}\rightarrow u$ in $L^{\infty}$?

If $\mathcal H$ is the closure of the set $D$ of divergence-free smooth functions in $L^2$, then $H_0^1∩\mathcal H$ is the closure of $D$ in $H_0^1$

Different definitions of Besov norm/space

How to think of Sobolev spaces $W^{k, p}$ for a function that is no longer an element of $W^{k, p}$ for $p$ greater than some number?

$W^{1,1}\subseteq AC$ and a certain property implies BV: why?

Does $f \in W^{2,p}(a,b)$ imply $f \in C^1([a,b])$?

The eigenvalue of Laplace problem on a domain with a line removed

The eigenfunction of modified 1-laplace equation

Why is $W^{k,p}(\Omega)$ the completion of $(\widetilde{C}^k(\Omega)$ instead of $W^{k,p}(\Omega) = (\widetilde{C}^k(\Omega)$?

Does the validity of Sobolev inequality on a domain imply it's a Sobolev extension domain?

I don't see why $W^{1, 2}(\partial D)$ being compactly embedded in $L^2(\partial D)$ lets us show an operator is Fredholm of index zero.

Weak derivative of maximum

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