Question

How are Sobolev spaces on compact Riemannian manifolds defined?

score 331 · Answer 1 · 2026-03-25 09:26:38

331

Views

How are Sobolev spaces on compact Riemannian manifolds defined?

Published on 25 Mar 2026 - 9:26

score 44 · Answer 2 · 2019-06-05 12:21:15

44

Views

Looking for a convergent sequence in $W^{1,2}[0,\infty)$ with some properties.

Published on 05 Jun 2019 - 12:21

score 420 · Answer 3 · 2026-03-25 07:45:03

420

Views

Is the definition of the Sobolev space H^1(M) on a compact manifold that simple?

Published on 25 Mar 2026 - 7:45

score 81 · Answer 4 · 2026-03-28 14:00:20

81

Views

Does anyone know any books provide complete picture of mathematical spaces, hierarchical view, relations, natural progression among them

Published on 28 Mar 2026 - 14:00

score 140 · Answer 5 · 2019-06-07 12:32:08

140

Views

Extension of a Sobolev Function

Published on 07 Jun 2019 - 12:32

score 1.2k · Answer 6 · 2026-03-26 01:11:54

1.2k

Views

If compact embedding $H^1_0(\Omega) \hookrightarrow H^{-1}(\Omega)$ is not surjective, how can $H^{-1}(\Omega)$ be the dual of $H^1_0(\Omega)$?

Published on 26 Mar 2026 - 1:11

score 56 · Answer 7 · 2026-03-25 08:05:56

56

Views

weak solution to non-homogeneous initial-boundary value problem

Published on 25 Mar 2026 - 8:05

score 88 · Answer 8 · 2019-06-10 07:36:27

88

Views

PDE's as minimisation problems

Published on 10 Jun 2019 - 7:36

score 119 · Answer 9 · 2026-03-26 09:41:55

119

Views

Strict inequality of the H1 seminorm of a curve emerging from a convex set and its convex projection

Published on 26 Mar 2026 - 9:41

score 98 · Answer 10 · 2019-06-12 10:46:50

98

Views

Why chose $H^{-1}(\Omega)$ instead of $L^2(\Omega)$?

Published on 12 Jun 2019 - 10:46

score 97 · Answer 11 · 2019-06-12 13:08:13

97

Views

Composition of Sobolev map and smooth function.

Published on 12 Jun 2019 - 13:08

score 67 · Answer 12 · 2026-03-25 17:45:06

67

Views

Definition de $L^1((0,T);W^{1,\infty}(\mathbb R))$.

Published on 25 Mar 2026 - 17:45

score 93 · Answer 13 · 2026-03-25 03:04:02

93

Views

Properties of Functions in $W^{1,p}(\Omega)$ and Their Weak Derivatives

Published on 25 Mar 2026 - 3:04

score 27 · Answer 14 · 2026-03-28 01:12:45

27

Views

approximating functions in $W^{1,2}$ with Lipschitz functions with image contained in fixed ball

Published on 28 Mar 2026 - 1:12

score 59 · Answer 15 · 2026-03-30 03:38:27

59

Views

Showing that $u\in H^k(\mathbb{R}^n)\Leftrightarrow <\xi>^k\hat{u}\in L^2(\mathbb{R}^n)$ Taylor Michael.

Published on 30 Mar 2026 - 3:38

List Question

How are Sobolev spaces on compact Riemannian manifolds defined?

Looking for a convergent sequence in $W^{1,2}[0,\infty)$ with some properties.

Is the definition of the Sobolev space H^1(M) on a compact manifold that simple?

Does anyone know any books provide complete picture of mathematical spaces, hierarchical view, relations, natural progression among them

Extension of a Sobolev Function

If compact embedding $H^1_0(\Omega) \hookrightarrow H^{-1}(\Omega)$ is not surjective, how can $H^{-1}(\Omega)$ be the dual of $H^1_0(\Omega)$?

weak solution to non-homogeneous initial-boundary value problem

PDE's as minimisation problems

Strict inequality of the H1 seminorm of a curve emerging from a convex set and its convex projection

Why chose $H^{-1}(\Omega)$ instead of $L^2(\Omega)$?

Composition of Sobolev map and smooth function.

Definition de $L^1((0,T);W^{1,\infty}(\mathbb R))$.

Properties of Functions in $W^{1,p}(\Omega)$ and Their Weak Derivatives

approximating functions in $W^{1,2}$ with Lipschitz functions with image contained in fixed ball

Showing that $u\in H^k(\mathbb{R}^n)\Leftrightarrow <\xi>^k\hat{u}\in L^2(\mathbb{R}^n)$ Taylor Michael.

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