Question

Interpolation of derivatives in Sobolev spaces

score 311 · Answer 1 · 2026-04-17 06:55:33

311

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Interpolation of derivatives in Sobolev spaces

Published on 17 Apr 2026 - 6:55

score 296 · Answer 2 · 2026-03-26 16:10:15

296

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About the dual space of $V=\{u\in H_0^1(\Omega): \text{div}u=0 \}$ and its relations to $H^{-1}(\Omega)$.

Published on 26 Mar 2026 - 16:10

score 218 · Answer 3 · 2026-04-14 06:25:38

218

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If $u_n \to u$ in $H^1$ and $\Delta u_n$ is bounded in $L^\infty$ is $u \in H^2$?

Published on 14 Apr 2026 - 6:25

score 1.1k · Answer 4 · 2026-03-27 02:02:49

1.1k

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Question about the proof of General Sobolev Inequality in P.D.E. by Evan

Published on 27 Mar 2026 - 2:02

score 91 · Answer 5 · 2026-04-16 06:32:31

91

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Relation of $\lVert \dot u \rVert_{W^1(\Omega)}$ to $ \lVert u \rVert_{W^1(\Omega)}$

Published on 16 Apr 2026 - 6:32

score 54 · Answer 6 · 2026-04-11 19:29:26

54

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Is this a Sobolev function?

Published on 11 Apr 2026 - 19:29

score 35 · Answer 7 · 2026-04-15 04:19:48

35

Views

Partial Sobolev function: if $f(x,y) \in W^{1,1}((0,1)\times (0,1))$ and $\partial_{x}f(x,y) = 0$, there is $h(y) \in L^1(0,1)$ s.t. $f(x,y) = h(y)$

Published on 15 Apr 2026 - 4:19

score 47 · Answer 8 · 2026-04-14 20:18:45

47

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Is $\langle \mu, z \rangle_{H^{-1}, H^1}=0$ if $\mu \in H^{-1}$ has support in a subdomain on which $z$ vanishes?

Published on 14 Apr 2026 - 20:18

score 539 · Answer 9 · 2026-04-23 06:21:12

539

Views

A function in $H(div)$ not in $H^1$

Published on 23 Apr 2026 - 6:21

score 541 · Answer 10 · 2026-04-13 18:58:12

541

Views

PDE Estimate for Poisson Equation

Published on 13 Apr 2026 - 18:58

score 1k · Answer 11 · 2026-03-25 23:09:00

1k

Views

Frechet and Gateaux derivative of integrals

Published on 25 Mar 2026 - 23:09

score 165 · Answer 12 · 2026-04-14 13:30:18

165

Views

If $u\in H_0^1(\Omega)$ satisfies $-\Delta u=f$, with $f\in C^{\alpha}(\bar{\Omega})$, then $u\in C^{2,\alpha}(\bar{\Omega})$.

Published on 14 Apr 2026 - 13:30

score 256 · Answer 13 · 2026-04-12 22:54:04

256

Views

Can Sobolev spaces with $1 \le p < 2$ be defined in terms of Fourier transforms?

Published on 12 Apr 2026 - 22:54

score 89 · Answer 14 · 2026-03-28 08:36:30

89

Views

Can we use the defining property of weak derivatives when integrating over general measurable sets?

Published on 28 Mar 2026 - 8:36

score 97 · Answer 15 · 2026-03-26 19:18:57

97

Views

$\partial_t u \in W^{-1,\infty}\left(0,T;W^{-1,2}(\Omega)\right)$ where $u$ weak solution of Navier-Stokes

Published on 26 Mar 2026 - 19:18

List Question

Interpolation of derivatives in Sobolev spaces

About the dual space of $V=\{u\in H_0^1(\Omega): \text{div}u=0 \}$ and its relations to $H^{-1}(\Omega)$.

If $u_n \to u$ in $H^1$ and $\Delta u_n$ is bounded in $L^\infty$ is $u \in H^2$?

Question about the proof of General Sobolev Inequality in P.D.E. by Evan

Relation of $\lVert \dot u \rVert_{W^1(\Omega)}$ to $ \lVert u \rVert_{W^1(\Omega)}$

Is this a Sobolev function?

Partial Sobolev function: if $f(x,y) \in W^{1,1}((0,1)\times (0,1))$ and $\partial_{x}f(x,y) = 0$, there is $h(y) \in L^1(0,1)$ s.t. $f(x,y) = h(y)$

Is $\langle \mu, z \rangle_{H^{-1}, H^1}=0$ if $\mu \in H^{-1}$ has support in a subdomain on which $z$ vanishes?

A function in $H(div)$ not in $H^1$

PDE Estimate for Poisson Equation

Frechet and Gateaux derivative of integrals

If $u\in H_0^1(\Omega)$ satisfies $-\Delta u=f$, with $f\in C^{\alpha}(\bar{\Omega})$, then $u\in C^{2,\alpha}(\bar{\Omega})$.

Can Sobolev spaces with $1 \le p < 2$ be defined in terms of Fourier transforms?

Can we use the defining property of weak derivatives when integrating over general measurable sets?

$\partial_t u \in W^{-1,\infty}\left(0,T;W^{-1,2}(\Omega)\right)$ where $u$ weak solution of Navier-Stokes

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