Question

The limit of a Lebesgue integral

score 179 · Answer 1 · 2026-04-12 21:12:04

179

Views

The limit of a Lebesgue integral

Published on 12 Apr 2026 - 21:12

score 32 · Answer 2 · 2026-04-12 21:20:46

32

Views

Intersection of compact sets in different spaces

Published on 12 Apr 2026 - 21:20

score 34 · Answer 3 · 2026-04-11 16:21:48

34

Views

Is convolution integrable in $L_1(\mathbb{R}^n)$?

Published on 11 Apr 2026 - 16:21

score 859 · Answer 4 · 2026-04-18 23:18:17

859

Views

Completeness of weighted $L^p$ spaces

Published on 18 Apr 2026 - 23:18

score 45 · Answer 5 · 2026-05-14 23:20:29

45

Views

How to prove that normed space is complete?

Published on 14 May 2026 - 23:20

score 162 · Answer 6 · 2026-05-14 23:20:52

162

Views

Equivalent definitions of Sobolev space on manifold and references

Published on 14 May 2026 - 23:20

score 188 · Answer 7 · 2026-04-10 18:21:52

188

Views

Show existence of bounded linear functional

Published on 10 Apr 2026 - 18:21

score 138 · Answer 8 · 2026-04-16 22:52:54

138

Views

Show that $C^\infty(0,T; L^2(\Omega(t)))$ is dense in $L^2(0,T; L^2(\Omega(t)))$.

Published on 16 Apr 2026 - 22:52

score 245 · Answer 9 · 2026-04-09 16:17:15

245

Views

Let $X$ be a locally compact Polish space. Is the space of continuous functions with compact support dense in that of $\mu$-integrable functions?

Published on 09 Apr 2026 - 16:17

score 59 · Answer 10 · 2026-04-08 23:26:13

59

Views

If $T$ is a compact operator and $S$ is a bounded operator then $TS-ST$ cannot be the identity operator.

Published on 08 Apr 2026 - 23:26

score 51 · Answer 11 · 2026-04-14 22:18:28

51

Views

Evaluate integral wrt Lebesgue measure and find the L^p space if it exists

Published on 14 Apr 2026 - 22:18

score 32 · Answer 12 · 2026-04-16 05:21:47

32

Views

Extending weak-type linear operator from $L^{p}\cap L^{q}$ to $L^{r}$ where $1\leq p<r<q<\infty$

Published on 16 Apr 2026 - 5:21

score 93 · Answer 13 · 2026-04-13 17:01:55

93

Views

Prove the uniqueness of $u\in H_0^1(\Omega)$ with $\Delta u=\vert u\vert^{q-1}u+f$ in $\Omega$ with $\Omega$ as a bounded domain with smooth boundary.

Published on 13 Apr 2026 - 17:01

score 73 · Answer 14 · 2026-04-15 06:39:06

73

Views

Is this shorter attempt on the existence of the maximizer in Kantorovich duality is correct?

Published on 15 Apr 2026 - 6:39

score 84 · Answer 15 · 2026-05-15 00:37:54

84

Views

Proving $||f||^2_{L^2(\mathbb R^2)}\le 10||f||_{L^1(\mathbb R^2)}||\nabla f||_{L^2(\mathbb R^2)}$ with $f\in C^1,L^1\cap L^2$ and $\nabla f\in L^2$.

Published on 15 May 2026 - 0:37

List Question

The limit of a Lebesgue integral

Intersection of compact sets in different spaces

Is convolution integrable in $L_1(\mathbb{R}^n)$?

Completeness of weighted $L^p$ spaces

How to prove that normed space is complete?

Equivalent definitions of Sobolev space on manifold and references

Show existence of bounded linear functional

Show that $C^\infty(0,T; L^2(\Omega(t)))$ is dense in $L^2(0,T; L^2(\Omega(t)))$.

Let $X$ be a locally compact Polish space. Is the space of continuous functions with compact support dense in that of $\mu$-integrable functions?

If $T$ is a compact operator and $S$ is a bounded operator then $TS-ST$ cannot be the identity operator.

Evaluate integral wrt Lebesgue measure and find the L^p space if it exists

Extending weak-type linear operator from $L^{p}\cap L^{q}$ to $L^{r}$ where $1\leq p<r<q<\infty$

Prove the uniqueness of $u\in H_0^1(\Omega)$ with $\Delta u=\vert u\vert^{q-1}u+f$ in $\Omega$ with $\Omega$ as a bounded domain with smooth boundary.

Is this shorter attempt on the existence of the maximizer in Kantorovich duality is correct?

Proving $||f||^2_{L^2(\mathbb R^2)}\le 10||f||_{L^1(\mathbb R^2)}||\nabla f||_{L^2(\mathbb R^2)}$ with $f\in C^1,L^1\cap L^2$ and $\nabla f\in L^2$.

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