List questions from sobolev-spaces

Published on 15 Apr 2026 - 20:20

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Proof that function is in $H^1$

Published on 11 Apr 2026 - 6:09

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What happens when you change space of test functions associated with weak derivatives?

Published on 13 Apr 2026 - 12:17

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Why is $H^1 \neq H_0^1$?

Published on 16 Apr 2026 - 3:04

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Simple heat equation, solution regularity

Published on 10 Apr 2026 - 19:13

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Distributional traces

Published on 21 Apr 2026 - 5:21

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for what values $\alpha\in \Bbb{R}$ we have $v_{\alpha}\in H^{1}(\Omega)$?

Published on 12 Apr 2026 - 9:17

62

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Extention of functions in Sobolev spaces

Published on 15 Apr 2026 - 6:12

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adjoint operator in Sobolev space

Published on 09 Apr 2026 - 11:55

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An inequality : $ \| u^3 \|_{H^3} \leq C ( \| u \|_{L^\infty}^2 + \| \partial_x u \|_{L^\infty}^2 ) \| u \|_{H^3}$

Published on 14 Apr 2026 - 20:54

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Difference Quotient Proof

Published on 16 Apr 2026 - 22:40

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Stampacchia Theorem: $\nabla G(u)=G'(u)\nabla u$?

Published on 16 Apr 2026 - 10:40

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Decay of $H^1(\mathbb{R}^n)$ functions

Published on 14 Apr 2026 - 9:56

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An example of self-adjoint and positive operator

Published on 10 Apr 2026 - 12:51

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Proving that a certain function is in $W^{1,n}(B(0,1))$

Published on 16 Apr 2026 - 15:16

List Question

There exist a function $u(x)\in C([0,1]),~ u(0)=u(1)=0$ such that $u \notin H_{0}^{1}((0,1))$?

Proof that function is in $H^1$

What happens when you change space of test functions associated with weak derivatives?

Why is $H^1 \neq H_0^1$?

Simple heat equation, solution regularity

Distributional traces

for what values $\alpha\in \Bbb{R}$ we have $v_{\alpha}\in H^{1}(\Omega)$?

Extention of functions in Sobolev spaces

adjoint operator in Sobolev space

An inequality : $ \| u^3 \|_{H^3} \leq C ( \| u \|_{L^\infty}^2 + \| \partial_x u \|_{L^\infty}^2 ) \| u \|_{H^3}$

Difference Quotient Proof

Stampacchia Theorem: $\nabla G(u)=G'(u)\nabla u$?

Decay of $H^1(\mathbb{R}^n)$ functions

An example of self-adjoint and positive operator

Proving that a certain function is in $W^{1,n}(B(0,1))$

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