Question

A problem for laplace operator in Sobolev space

score 378 · Answer 1 · 2026-04-08 10:48:47

378

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A problem for laplace operator in Sobolev space

Published on 08 Apr 2026 - 10:48

score 406 · Answer 2 · 2026-04-07 17:00:53

406

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Is trace operator is invertible?

Published on 07 Apr 2026 - 17:00

score 16.9k · Answer 3 · 2015-01-07 14:10:52

16.9k

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The Sobolev Space $H^{1/2}$

Published on 07 Jan 2015 - 14:10

score 163 · Answer 4 · 2026-03-30 17:11:29

163

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Proof of existence of trace map $T:H^1(\mathbb{R}^n_+) \to H^{\frac 12}(\mathbb{R}^{n-1})$ not using the Fourier transform

Published on 30 Mar 2026 - 17:11

score 820 · Answer 5 · 2015-01-08 01:45:37

820

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A generalization of the problem: "$\|\Delta u\|_{L^2}$ is an equivalent norm for standard $H^2$ norm in space $H_0^1\cap H^2$

Published on 08 Jan 2015 - 1:45

score 185 · Answer 6 · 2015-01-08 13:41:25

185

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The averages, near the boundary, of a function $u\in W_0^{1,p}(\Omega)$, converge to zero.

Published on 08 Jan 2015 - 13:41

score 311 · Answer 7 · 2026-04-08 03:06:21

311

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Convergence in dual of Sobolev space

Published on 08 Apr 2026 - 3:06

score 2.2k · Answer 8 · 2026-03-30 17:07:37

2.2k

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The Trace Theorem for $W^{1,p}$ functions

Published on 30 Mar 2026 - 17:07

score 586 · Answer 9 · 2026-03-31 16:57:17

586

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Deriving $|u(x)-u(y)|\le|x-y|^{1-\frac 1p}\left(\int_0^1 |u'|^p \, dt \right)^{1/p}$

Published on 31 Mar 2026 - 16:57

score 46 · Answer 10 · 2015-01-11 19:16:04

46

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Inequality involving $H^s$ and $L^2$.

Published on 11 Jan 2015 - 19:16

score 143 · Answer 11 · 2015-01-12 15:52:07

143

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$\int_\Omega |\nabla u^+|^2 \, dx$ is not differentiable with respect to $u$ in $W_0^{1,2}(\Omega)$

Published on 12 Jan 2015 - 15:52

score 1.7k · Answer 12 · 2026-03-31 16:57:26

1.7k

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Estimate $L^{2p}$ norm of the gradient by the supremum of the function and $L^p$ norm of the Hessian

Published on 31 Mar 2026 - 16:57

score 190 · Answer 13 · 2026-03-29 06:00:37

190

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Using Mac Shane's Lemma

Published on 29 Mar 2026 - 6:00

score 379 · Answer 14 · 2015-01-13 17:36:31

379

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Why does this completion of a Sobolev space contain constant functions? Please explain text.

Published on 13 Jan 2015 - 17:36

score 497 · Answer 15 · 2015-01-13 19:37:09

497

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Proof of weak derivatives in Evans PDE?

Published on 13 Jan 2015 - 19:37

List Question

A problem for laplace operator in Sobolev space

Is trace operator is invertible?

The Sobolev Space $H^{1/2}$

Proof of existence of trace map $T:H^1(\mathbb{R}^n_+) \to H^{\frac 12}(\mathbb{R}^{n-1})$ not using the Fourier transform

A generalization of the problem: "$\|\Delta u\|_{L^2}$ is an equivalent norm for standard $H^2$ norm in space $H_0^1\cap H^2$

The averages, near the boundary, of a function $u\in W_0^{1,p}(\Omega)$, converge to zero.

Convergence in dual of Sobolev space

The Trace Theorem for $W^{1,p}$ functions

Deriving $|u(x)-u(y)|\le|x-y|^{1-\frac 1p}\left(\int_0^1 |u'|^p \, dt \right)^{1/p}$

Inequality involving $H^s$ and $L^2$.

$\int_\Omega |\nabla u^+|^2 \, dx$ is not differentiable with respect to $u$ in $W_0^{1,2}(\Omega)$

Estimate $L^{2p}$ norm of the gradient by the supremum of the function and $L^p$ norm of the Hessian

Using Mac Shane's Lemma

Why does this completion of a Sobolev space contain constant functions? Please explain text.

Proof of weak derivatives in Evans PDE?

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