Question

Density of a space of functions in Sobolev space

score 94 · Answer 1 · 2023-03-03 03:09:05

94

Views

Density of a space of functions in Sobolev space

Published on 03 Mar 2023 - 3:09

score 38 · Answer 2 · 2023-03-03 22:40:27

38

Views

Existence of function in subset of Sobolev space

Published on 03 Mar 2023 - 22:40

score 109 · Answer 3 · 2023-03-03 23:29:42

109

Views

Difficulty with proof of Rellich-Kondrachov Compactness Theorem

Published on 03 Mar 2023 - 23:29

score 87 · Answer 4 · 2026-03-25 08:07:00

87

Views

Fractional Sobolev space with zero boundary

Published on 25 Mar 2026 - 8:07

score 35 · Answer 5 · 2026-03-25 17:24:35

35

Views

Weak derivative as unbounded operator on $H^{-1}(0,T)$

Published on 25 Mar 2026 - 17:24

score 144 · Answer 6 · 2023-03-05 09:01:45

144

Views

Weak convergence in $W^{1,2}$ implies strong convergence under extra condition?

Published on 05 Mar 2023 - 9:01

score 72 · Answer 7 · 2026-03-31 21:51:58

72

Views

Spectrum of $A u=i u^{\prime}$ on differing domains in $L^2([0,1])$

Published on 31 Mar 2026 - 21:51

score 44 · Answer 8 · 2026-03-26 17:43:36

44

Views

Implication in the space $W^{1,p}_0$

Published on 26 Mar 2026 - 17:43

score 39 · Answer 9 · 2026-04-01 13:08:09

39

Views

If the distributional derivative of a distribution is a funcion, is the original distribution a function too?

Published on 01 Apr 2026 - 13:08

score 30 · Answer 10 · 2026-03-26 17:33:37

30

Views

How does the constant in $\|u\|_{L^p} \leq C \|\Delta u \| _{L^p}$ depend on the smallest eigenvalue of the Laplacian?

Published on 26 Mar 2026 - 17:33

score 47 · Answer 11 · 2023-03-08 13:40:59

47

Views

Show $\int_{0}^{L}\int_{0}^{\infty}g(s)\partial_{s}\eta_{x}(x,s)u_{x}dsdx = -\int_{0}^{L}\int_{0}^{\infty}g^{\prime}(s)\eta_{x}(x,s)u_{x}dsdx $

Published on 08 Mar 2023 - 13:40

score 88 · Answer 12 · 2023-03-12 11:16:33

88

Views

How to show $ \|fg\|_{L^2}\leq \|\partial_{x_1}f\|_{L^2}\|g\|_{L^2}+\|f\|_{L^2}\|\partial_{x_2}g\|_{L^2} $?

Published on 12 Mar 2023 - 11:16

score 82 · Answer 13 · 2026-03-26 11:06:47

82

Views

$L^{1}$ bounded solution of elliptic equation implies $L^{\infty}$ boundedness

Published on 26 Mar 2026 - 11:06

score 58 · Answer 14 · 2026-03-25 11:19:02

58

Views

Function in $W^{1,2}(\mathbb{R}^3)$, but not in $L^1(\mathbb{R^3})$

Published on 25 Mar 2026 - 11:19

score 63 · Answer 15 · 2026-03-25 11:22:44

63

Views

Minimizer of a functional over a set

Published on 25 Mar 2026 - 11:22

List Question

Density of a space of functions in Sobolev space

Existence of function in subset of Sobolev space

Difficulty with proof of Rellich-Kondrachov Compactness Theorem

Fractional Sobolev space with zero boundary

Weak derivative as unbounded operator on $H^{-1}(0,T)$

Weak convergence in $W^{1,2}$ implies strong convergence under extra condition?

Spectrum of $A u=i u^{\prime}$ on differing domains in $L^2([0,1])$

Implication in the space $W^{1,p}_0$

If the distributional derivative of a distribution is a funcion, is the original distribution a function too?

How does the constant in $\|u\|_{L^p} \leq C \|\Delta u \| _{L^p}$ depend on the smallest eigenvalue of the Laplacian?

Show $\int_{0}^{L}\int_{0}^{\infty}g(s)\partial_{s}\eta_{x}(x,s)u_{x}dsdx = -\int_{0}^{L}\int_{0}^{\infty}g^{\prime}(s)\eta_{x}(x,s)u_{x}dsdx $

How to show $ \|fg\|_{L^2}\leq \|\partial_{x_1}f\|_{L^2}\|g\|_{L^2}+\|f\|_{L^2}\|\partial_{x_2}g\|_{L^2} $?

$L^{1}$ bounded solution of elliptic equation implies $L^{\infty}$ boundedness

Function in $W^{1,2}(\mathbb{R}^3)$, but not in $L^1(\mathbb{R^3})$

Minimizer of a functional over a set

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