Question

$\lim_{p \to \infty} \bigg ( \sum_{i=1}^m \lambda_i |x_i|^p \bigg )^{1/p} = \max _{1 \leq i\leq m} |x_{i}|$

score 47 · Answer 1 · 2023-03-29 23:23:55

47

Views

$\lim_{p \to \infty} \bigg ( \sum_{i=1}^m \lambda_i |x_i|^p \bigg )^{1/p} = \max _{1 \leq i\leq m} |x_{i}|$

Published on 29 Mar 2023 - 23:23

score 86 · Answer 2 · 2026-03-27 01:44:32

86

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Sub-level sets of $BV$ functions - references and results

Published on 27 Mar 2026 - 1:44

score 63 · Answer 3 · 2023-03-30 10:50:09

63

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Brezis's Exercise 4.6: is the assumption $\mu(\Omega) < \infty$ necessary?

Published on 30 Mar 2023 - 10:50

score 38 · Answer 4 · 2026-03-25 22:03:46

38

Views

Weak star convegence in $L^{\infty}(0,T;L^2(\Omega))$ implies almost everywhere convergence?

Published on 25 Mar 2026 - 22:03

score 61 · Answer 5 · 2026-03-29 04:34:29

61

Views

Use cases for $L^p$ and $l^p$ spaces where $p\neq 1,2,\infty$

Published on 29 Mar 2026 - 4:34

score 159 · Answer 6 · 2026-04-08 20:55:45

159

Views

Compact set on $L^p([0,1])$

Published on 08 Apr 2026 - 20:55

score 75 · Answer 7 · 2026-04-07 06:36:19

75

Views

The representation of a linear continuous map $T:L^p(\Omega) \to L^q(\Omega)$

Published on 07 Apr 2026 - 6:36

score 79 · Answer 8 · 2023-04-02 11:21:18

79

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Example of a function in $L^{\infty}-L^p$

Published on 02 Apr 2023 - 11:21

score 67 · Answer 9 · 2026-04-07 06:27:07

67

Views

Brezis' Exercise 4.7

Published on 07 Apr 2026 - 6:27

score 92 · Answer 10 · 2026-04-07 06:27:07

92

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Brezis' Exercise 4.13

Published on 07 Apr 2026 - 6:27

score 48 · Answer 11 · 2023-04-02 17:27:01

48

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Assume $f(\omega) \in D(J)$ for $\mu$-a.e. $\omega \in \Omega$. How to obtain $\frac{1}{\mu(\Omega)} \int_\Omega f \, \mathrm d \mu\in D(J)$?

Published on 02 Apr 2023 - 17:27

score 39 · Answer 12 · 2026-03-26 19:02:00

39

Views

Must solutions to the time-independent Schrodinger equation that have discrete spectra or negative eigenvalues be square-integrable?

Published on 26 Mar 2026 - 19:02

score 58 · Answer 13 · 2026-02-23 11:39:15

58

Views

Brezis' Exercise 4.10.1 and 4.10.2

Published on 23 Feb 2026 - 11:39

score 95 · Answer 14 · 2026-03-29 20:06:21

95

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Brezis' Exercise 4.10.3: can we pick such a measurable $u_n$?

Published on 29 Mar 2026 - 20:06

score 46 · Answer 15 · 2026-04-07 06:33:37

46

Views

Let $(f_n) \subset L^1(\Omega)$ such that $f_n \le f_{n+1}$ and $\sup_n \int f_n \le r$. Does $f_n \to f$ a.e. imply $f \in L^1 (\Omega)$?

Published on 07 Apr 2026 - 6:33

List Question

$\lim_{p \to \infty} \bigg ( \sum_{i=1}^m \lambda_i |x_i|^p \bigg )^{1/p} = \max _{1 \leq i\leq m} |x_{i}|$

Sub-level sets of $BV$ functions - references and results

Brezis's Exercise 4.6: is the assumption $\mu(\Omega) < \infty$ necessary?

Weak star convegence in $L^{\infty}(0,T;L^2(\Omega))$ implies almost everywhere convergence?

Use cases for $L^p$ and $l^p$ spaces where $p\neq 1,2,\infty$

Compact set on $L^p([0,1])$

The representation of a linear continuous map $T:L^p(\Omega) \to L^q(\Omega)$

Example of a function in $L^{\infty}-L^p$

Brezis' Exercise 4.7

Brezis' Exercise 4.13

Assume $f(\omega) \in D(J)$ for $\mu$-a.e. $\omega \in \Omega$. How to obtain $\frac{1}{\mu(\Omega)} \int_\Omega f \, \mathrm d \mu\in D(J)$?

Must solutions to the time-independent Schrodinger equation that have discrete spectra or negative eigenvalues be square-integrable?

Brezis' Exercise 4.10.1 and 4.10.2

Brezis' Exercise 4.10.3: can we pick such a measurable $u_n$?

Let $(f_n) \subset L^1(\Omega)$ such that $f_n \le f_{n+1}$ and $\sup_n \int f_n \le r$. Does $f_n \to f$ a.e. imply $f \in L^1 (\Omega)$?

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