Question

Let $u_n \rightharpoonup u$ in $W^{2,p}(\Omega)$ for sufficiently large $p$. Does $\Delta u_n^+ \rightharpoonup \Delta u^+$ in $L^2(\Omega)$?

score 58 · Answer 1 · 2018-05-31 12:20:18

58

Views

Let $u_n \rightharpoonup u$ in $W^{2,p}(\Omega)$ for sufficiently large $p$. Does $\Delta u_n^+ \rightharpoonup \Delta u^+$ in $L^2(\Omega)$?

Published on 31 May 2018 - 12:20

score 35 · Answer 2 · 2018-06-02 12:32:49

35

Views

Estimate the Rayleigh quotient of rectangular domain from below

Published on 02 Jun 2018 - 12:32

score 284 · Answer 3 · 2026-03-25 00:07:39

284

Views

Is being in the Sobolev space of power $\frac{d}{2}$ necessary for having well defined point evaluations?

Published on 25 Mar 2026 - 0:07

score 58 · Answer 4 · 2018-06-04 09:30:32

58

Views

If a function belongs to $W^{k,p}(\Omega)$ for every $p$, does it belong to $W^{k,\infty}(\Omega)$?

Published on 04 Jun 2018 - 9:30

score 133 · Answer 5 · 2018-06-04 13:36:02

133

Views

$L^\infty$ estimate for $H^s$ functions in $\mathbb{R}$

Published on 04 Jun 2018 - 13:36

score 435 · Answer 6 · 2018-06-04 19:44:25

435

Views

Is the Sobolev space $H^1(K)$ the same as the space of continuous functions?

Published on 04 Jun 2018 - 19:44

score 71 · Answer 7 · 2018-06-05 13:41:28

71

Views

$f \in C^1$with bounded derivative

Published on 05 Jun 2018 - 13:41

score 196 · Answer 8 · 2018-06-06 09:15:58

196

Views

Evans 1st edition, exercise 7, chapter 5

Published on 06 Jun 2018 - 9:15

score 68 · Answer 9 · 2018-06-06 11:42:14

68

Views

Question about a proposition in Brezis' Sobolev Spaces

Published on 06 Jun 2018 - 11:42

score 54 · Answer 10 · 2018-06-08 05:16:11

54

Views

A uniform limit of Sobolev functions is Sobolev?

Published on 08 Jun 2018 - 5:16

score 162 · Answer 11 · 2018-06-09 23:45:41

162

Views

The Sobolev completion of $C_c^\infty(\Bbb R^n)$ can be embedded in $L^2(\Bbb R^n)$

Published on 09 Jun 2018 - 23:45

score 50 · Answer 12 · 2018-06-10 15:01:03

50

Views

Integral of function in $R^2$ - Sobolev space

Published on 10 Jun 2018 - 15:01

score 164 · Answer 13 · 2018-06-10 16:00:40

164

Views

Prove that $\lim\limits_{|x|\rightarrow \infty} u(x) = 0$ for $u \in W^{1,p}(\mathbb{R}^n).$

Published on 10 Jun 2018 - 16:00

score 90 · Answer 14 · 2018-06-11 19:33:28

90

Views

Consider the following function ρ (f) on W1,2[0,1]

Published on 11 Jun 2018 - 19:33

score 100 · Answer 15 · 2018-06-12 05:24:08

100

Views

The Dirichlet problem for second order elliptic operators

Published on 12 Jun 2018 - 5:24

List Question

Let $u_n \rightharpoonup u$ in $W^{2,p}(\Omega)$ for sufficiently large $p$. Does $\Delta u_n^+ \rightharpoonup \Delta u^+$ in $L^2(\Omega)$?

Estimate the Rayleigh quotient of rectangular domain from below

Is being in the Sobolev space of power $\frac{d}{2}$ necessary for having well defined point evaluations?

If a function belongs to $W^{k,p}(\Omega)$ for every $p$, does it belong to $W^{k,\infty}(\Omega)$?

$L^\infty$ estimate for $H^s$ functions in $\mathbb{R}$

Is the Sobolev space $H^1(K)$ the same as the space of continuous functions?

$f \in C^1$with bounded derivative

Evans 1st edition, exercise 7, chapter 5

Question about a proposition in Brezis' Sobolev Spaces

A uniform limit of Sobolev functions is Sobolev?

The Sobolev completion of $C_c^\infty(\Bbb R^n)$ can be embedded in $L^2(\Bbb R^n)$

Integral of function in $R^2$ - Sobolev space

Prove that $\lim\limits_{|x|\rightarrow \infty} u(x) = 0$ for $u \in W^{1,p}(\mathbb{R}^n).$

Consider the following function ρ (f) on W1,2[0,1]

The Dirichlet problem for second order elliptic operators

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