List questions from sobolev-spaces

Published on 11 Apr 2026 - 0:23

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Identity map extends to an inclusion of Sobolev space into $L^2$

Published on 13 Apr 2026 - 10:20

281

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Composition rule for Sobolev spaces (Corollary 8.11, Brezis)

Published on 12 Apr 2026 - 13:00

299

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Does absolute value of a function belong to the same non-positive Besov/Sobolev space

Published on 11 Apr 2026 - 3:49

96

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Hodge decomposition theorem that uses a symmetric positive-definite matrix

Published on 13 Apr 2026 - 9:06

60

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Continuous maps between Banach spaces are smooth

Published on 09 Apr 2026 - 3:56

46

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Approximate $f\in \text{Lip}_K(\Omega)$ with $f\geq 0,f=0$ on $\partial \Omega$ by $f_n\in C_c(\Omega)\cap \text{Lip}_K(\Omega)$ with $f_n\geq 0$.

Published on 17 Apr 2026 - 1:08

57

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Vector spaces in PDE $C^{1}([0,+\infty) ; H) \cap C([0,+\infty) ; D(A))$

Published on 15 Apr 2026 - 1:57

245

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Definition and properties of $W^{-1,k}_{loc}(\Omega)$ space

Published on 15 Apr 2026 - 20:43

193

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Let $\Omega\subset \mathbb{R}^n$ be open and bounded. Is it true that $C^{0,1}(\Omega) \subset W^{1,\infty}(\Omega)$?

Published on 15 Apr 2026 - 4:51

30

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Is the following stronger Sobolev inequality true or not

Published on 12 Apr 2026 - 1:57

58

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Is $(-y,x)/\sqrt{x^2+y^2}$ in $[W^{1,\infty}([0,1]^2)]^2$

Published on 16 Apr 2026 - 3:50

179

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Existence of a weak solution to elliptic PDE with nonsmooth Robin boundary condition

Published on 14 Apr 2026 - 5:14

35

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Orthogonality in terms of two inner products in $W_0^{1,2}(U)$

Published on 06 May 2026 - 3:22

168

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An equality in Evans' PDE book chapter 9

Published on 11 Apr 2026 - 12:49

List Question

Representation of the magnetic field in 2D magnetostatics

Identity map extends to an inclusion of Sobolev space into $L^2$

Composition rule for Sobolev spaces (Corollary 8.11, Brezis)

Does absolute value of a function belong to the same non-positive Besov/Sobolev space

Hodge decomposition theorem that uses a symmetric positive-definite matrix

Continuous maps between Banach spaces are smooth

Approximate $f\in \text{Lip}_K(\Omega)$ with $f\geq 0,f=0$ on $\partial \Omega$ by $f_n\in C_c(\Omega)\cap \text{Lip}_K(\Omega)$ with $f_n\geq 0$.

Vector spaces in PDE $C^{1}([0,+\infty) ; H) \cap C([0,+\infty) ; D(A))$

Definition and properties of $W^{-1,k}_{loc}(\Omega)$ space

Let $\Omega\subset \mathbb{R}^n$ be open and bounded. Is it true that $C^{0,1}(\Omega) \subset W^{1,\infty}(\Omega)$?

Is the following stronger Sobolev inequality true or not

Is $(-y,x)/\sqrt{x^2+y^2}$ in $[W^{1,\infty}([0,1]^2)]^2$

Existence of a weak solution to elliptic PDE with nonsmooth Robin boundary condition

Orthogonality in terms of two inner products in $W_0^{1,2}(U)$

An equality in Evans' PDE book chapter 9

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