List questions from sobolev-spaces

Published on 15 Apr 2026 - 19:15

559

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Are piecewise polynomials $H^1$ functions?

Published on 12 Apr 2026 - 13:22

35

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Extending error bound from scalar functions to vector functions

Published on 11 Apr 2026 - 5:21

112

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Constant in Sobolev embedding theorem on the cube

Published on 14 Apr 2026 - 15:43

291

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Embedding $BV$ into $L^p$

Published on 12 Apr 2026 - 1:43

373

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Understanding the trace operator

Published on 09 Apr 2026 - 7:15

62

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Confusing definition of homogeneous Sobolev norm of order -1

Published on 12 Apr 2026 - 4:07

642

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$L^p$ regularity of elliptic operators

Published on 13 Apr 2026 - 6:41

119

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Sobolev's inequality for $u \in W^{1,p}(\Omega)$

Published on 17 Apr 2026 - 3:59

660

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Does the Sobolev space $W^{1,\infty}(\Omega)$ consist of all bounded Lipschitz functions on $\Omega$ when $\Omega$ is not quasiconvex?

Published on 15 Apr 2026 - 8:58

475

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Reference on Sobolev spaces $W^{k,p}(\Omega;\mathbb{R}^n)$

Published on 14 Apr 2026 - 23:51

3.9k

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Sobolev spaces with negative exponent

Published on 10 Apr 2026 - 0:21

156

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Weak lower semincontinuity of a functional with weak lower semicontinuity of $W^{1,2}$-norm

Published on 11 Apr 2026 - 18:11

165

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Example Domains that Break the Segment Property

Published on 17 Apr 2026 - 3:49

63

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Controlling supremum during weak convergence in Sobolev spaces

Published on 12 Apr 2026 - 7:29

List Question

Why $C_c^\infty(\mathbb{R})$ can be dense in different Banach space?

Are piecewise polynomials $H^1$ functions?

Extending error bound from scalar functions to vector functions

Constant in Sobolev embedding theorem on the cube

Embedding $BV$ into $L^p$

Understanding the trace operator

Confusing definition of homogeneous Sobolev norm of order -1

$L^p$ regularity of elliptic operators

Sobolev's inequality for $u \in W^{1,p}(\Omega)$

Does the Sobolev space $W^{1,\infty}(\Omega)$ consist of all bounded Lipschitz functions on $\Omega$ when $\Omega$ is not quasiconvex?

Reference on Sobolev spaces $W^{k,p}(\Omega;\mathbb{R}^n)$

Sobolev spaces with negative exponent

Weak lower semincontinuity of a functional with weak lower semicontinuity of $W^{1,2}$-norm

Example Domains that Break the Segment Property

Controlling supremum during weak convergence in Sobolev spaces

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