Question

Nash inequality : does $f\in L^1$ and $\nabla f \in L^2$ implies $f\in L^2$?

score 77 · Answer 1 · 2015-02-19 15:18:49

77

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Nash inequality : does $f\in L^1$ and $\nabla f \in L^2$ implies $f\in L^2$?

Published on 19 Feb 2015 - 15:18

score 1.8k · Answer 2 · 2015-02-20 16:34:35

1.8k

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Compactness Sobolev embedding for radial functions on $\mathbb{R}^N$

Published on 20 Feb 2015 - 16:34

score 259 · Answer 3 · 2015-02-21 15:44:22

259

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Sobolev embedding $W^{1,2}(\Omega)\subset L^p(\Omega)$ where $\Omega$ is a halfplane

Published on 21 Feb 2015 - 15:44

score 617 · Answer 4 · 2015-02-23 10:19:10

617

Views

Property implying weak differentiability

Published on 23 Feb 2015 - 10:19

score 1.1k · Answer 5 · 2015-02-23 20:49:30

1.1k

Views

Regularity properties of radially symmetric functions in Sobolev spaces.

Published on 23 Feb 2015 - 20:49

score 61 · Answer 6 · 2015-02-24 12:03:05

61

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Can $u\in W^{1,\infty}\cap H^1(\mathbb R^n)$ be approximated by a sequence $u_k\in C_0^{\infty}(\mathbb R^n)$ with $\|u_k\|_{1,\infty}$ bounded?

Published on 24 Feb 2015 - 12:03

score 96 · Answer 7 · 2026-03-28 14:05:38

96

Views

Boundedness of solutions for the Laplacian

Published on 28 Mar 2026 - 14:05

score 716 · Answer 8 · 2015-02-24 13:30:48

716

Views

Properties of Sobolev spaces $W^{k,\infty}(\Omega)$

Published on 24 Feb 2015 - 13:30

score 293 · Answer 9 · 2026-03-28 16:44:24

293

Views

Continuity of a nonlinear operator on fractional-order Sobolev spaces

Published on 28 Mar 2026 - 16:44

score 141 · Answer 10 · 2015-02-28 13:35:16

141

Views

Limit under the integral sign and partition of unity

Published on 28 Feb 2015 - 13:35

score 1.6k · Answer 11 · 2026-03-26 03:18:39

1.6k

Views

Riesz representation theorem in Sobolev spaces

Published on 26 Mar 2026 - 3:18

score 63 · Answer 12 · 2015-03-02 13:58:42

63

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Show that $2\nabla \sqrt f\,+\,x \sqrt f=0$ (a.e.). $\implies$ $\sqrt f\in \mathcal C_0$. (Derivatives are in weak sense)

Published on 02 Mar 2015 - 13:58

score 62 · Answer 13 · 2026-03-26 12:40:33

62

Views

Interchanging limits in $\lim\limits_{n \to \infty}\lim\limits_{j \to \infty}\int_0^T \langle u_n', w_j \rangle $ (weak time derivative)

Published on 26 Mar 2026 - 12:40

score 50 · Answer 14 · 2026-04-01 09:54:39

50

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Can we have $\|\nabla u \|_{L^1(B(0,1))}\leq \|\nabla u-\tilde{c} \|_{L^1(B(0,1))}$ for radially symmetric function?

Published on 01 Apr 2026 - 9:54

score 88 · Answer 15 · 2015-03-04 03:30:49

88

Views

Weak convergence and norm convergnce along a subsequnece in $H^1(\Omega)$

Published on 04 Mar 2015 - 3:30

List Question

Nash inequality : does $f\in L^1$ and $\nabla f \in L^2$ implies $f\in L^2$?

Compactness Sobolev embedding for radial functions on $\mathbb{R}^N$

Sobolev embedding $W^{1,2}(\Omega)\subset L^p(\Omega)$ where $\Omega$ is a halfplane

Property implying weak differentiability

Regularity properties of radially symmetric functions in Sobolev spaces.

Can $u\in W^{1,\infty}\cap H^1(\mathbb R^n)$ be approximated by a sequence $u_k\in C_0^{\infty}(\mathbb R^n)$ with $\|u_k\|_{1,\infty}$ bounded?

Boundedness of solutions for the Laplacian

Properties of Sobolev spaces $W^{k,\infty}(\Omega)$

Continuity of a nonlinear operator on fractional-order Sobolev spaces

Limit under the integral sign and partition of unity

Riesz representation theorem in Sobolev spaces

Show that $2\nabla \sqrt f\,+\,x \sqrt f=0$ (a.e.). $\implies$ $\sqrt f\in \mathcal C_0$. (Derivatives are in weak sense)

Interchanging limits in $\lim\limits_{n \to \infty}\lim\limits_{j \to \infty}\int_0^T \langle u_n', w_j \rangle $ (weak time derivative)

Can we have $\|\nabla u \|_{L^1(B(0,1))}\leq \|\nabla u-\tilde{c} \|_{L^1(B(0,1))}$ for radially symmetric function?

Weak convergence and norm convergnce along a subsequnece in $H^1(\Omega)$

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