Question

If $L^{\infty}$-norm of a set of Holder continuous functions is bounded, then does it imply that its $L^p$-norm is also bounded?

score 262 · Answer 1 · 2020-04-27 06:00:41

262

Views

If $L^{\infty}$-norm of a set of Holder continuous functions is bounded, then does it imply that its $L^p$-norm is also bounded?

Published on 27 Apr 2020 - 6:00

score 23 · Answer 2 · 2020-04-28 07:44:22

23

Views

Can you help me check the contruction of Operator J'_1: H^1(Omega\Gamma) -> H^1(Omega) right or not? where Gamma is a curve in Omega

Published on 28 Apr 2020 - 7:44

score 69 · Answer 3 · 2020-04-28 15:03:10

69

Views

Is this set closed in $H^1(\mathbb{R}^2)$?

Published on 28 Apr 2020 - 15:03

score 67 · Answer 4 · 2020-05-02 11:02:59

67

Views

Prove an inequality in the Sobolev space

Published on 02 May 2020 - 11:02

score 908 · Answer 5 · 2026-03-25 17:26:02

908

Views

Poincarè inequality in dimension $n=1$

Published on 25 Mar 2026 - 17:26

score 71 · Answer 6 · 2026-03-28 01:20:07

71

Views

Prove an integral equality by divergence theorem

Published on 28 Mar 2026 - 1:20

score 330 · Answer 7 · 2026-02-23 04:37:45

330

Views

A question in the proof that Lipchitz continuous functions implies $W^{1,\infty}$.

Published on 23 Feb 2026 - 4:37

score 110 · Answer 8 · 2026-03-25 06:26:39

110

Views

Determine if a function is in a fractional Sobolev space

Published on 25 Mar 2026 - 6:26

score 223 · Answer 9 · 2026-03-26 21:13:34

223

Views

Minimizing problem (1-dimensional phase transition)

Published on 26 Mar 2026 - 21:13

score 294 · Answer 10 · 2020-05-09 11:08:30

294

Views

What is the right embedding between $C^{\infty}_c (\mathbb{R}^n)$ and $H^1(\mathbb{R}^n)$?

Published on 09 May 2020 - 11:08

score 672 · Answer 11 · 2026-03-26 07:55:33

672

Views

Weak derivative of $\log\left(\log\left(1+\frac{1}{|x|}\right) \right)$

Published on 26 Mar 2026 - 7:55

score 313 · Answer 12 · 2020-05-11 08:10:23

313

Views

Not bounded function in $W^{1,1}(\mathbb{R})$

Published on 11 May 2020 - 8:10

score 624 · Answer 13 · 2026-03-26 07:50:56

624

Views

Not compact embeddings of Sobolev spaces in $L^p$

Published on 26 Mar 2026 - 7:50

score 36 · Answer 14 · 2020-05-13 16:49:49

36

Views

What does "by interpolation" mean and how to prove that $\vert x\vert^{\frac{1}{2}}$ is bounded from $H^{\frac{1}{2}}(\mathbb{R}^3)$?

Published on 13 May 2020 - 16:49

score 50 · Answer 15 · 2026-03-30 04:00:23

50

Views

Continuity of Neumann eigenvalues over smooth approximated domains

Published on 30 Mar 2026 - 4:00

List Question

If $L^{\infty}$-norm of a set of Holder continuous functions is bounded, then does it imply that its $L^p$-norm is also bounded?

Can you help me check the contruction of Operator J'_1: H^1(Omega\Gamma) -> H^1(Omega) right or not? where Gamma is a curve in Omega

Is this set closed in $H^1(\mathbb{R}^2)$?

Prove an inequality in the Sobolev space

Poincarè inequality in dimension $n=1$

Prove an integral equality by divergence theorem

A question in the proof that Lipchitz continuous functions implies $W^{1,\infty}$.

Determine if a function is in a fractional Sobolev space

Minimizing problem (1-dimensional phase transition)

What is the right embedding between $C^{\infty}_c (\mathbb{R}^n)$ and $H^1(\mathbb{R}^n)$?

Weak derivative of $\log\left(\log\left(1+\frac{1}{|x|}\right) \right)$

Not bounded function in $W^{1,1}(\mathbb{R})$

Not compact embeddings of Sobolev spaces in $L^p$

What does "by interpolation" mean and how to prove that $\vert x\vert^{\frac{1}{2}}$ is bounded from $H^{\frac{1}{2}}(\mathbb{R}^3)$?

Continuity of Neumann eigenvalues over smooth approximated domains

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