List questions from sobolev-spaces

Published on 14 Apr 2026 - 3:21

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How to prove that $H^1_{per}$ is an Hilbert space?

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function which is not Lipschitz but in $W^{1,\infty}$ on a domain with a slit

Published on 13 Apr 2026 - 14:58

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Is $H_0^1(\Omega)\subset C(\Omega)?$

Published on 12 Apr 2026 - 8:01

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Seeking references regarding Zero Extension of Sobolev ($W_0^{1,2}$) functions on a compact domain on $C^\infty$ Riemannian manifold

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The Heat Equation in Brezis' book

Published on 10 Apr 2026 - 4:02

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Question about the decay of $f\in W^{1,2}(\mathbb{R}^2)$

Published on 14 Apr 2026 - 0:41

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Do $u\in H^1(\Omega)$ and $\Delta u\in L^2(\Omega)$ imply $u\in H^2(\Omega)$?

Published on 13 Apr 2026 - 11:29

58

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What do we say about the Stokes Operator $-P \Delta$ on Morrey Spaces?

Published on 11 Apr 2026 - 21:26

175

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Weak l.s.c. of $L^2$-norm on $W^{1,2}_0(\Omega)$

Published on 12 Apr 2026 - 8:33

37

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Identification of $L^2(0,T;H^2(\Omega))$ with $L^\infty(Q_T)$

Published on 17 Apr 2026 - 15:35

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inverse laplace operator bounded

Published on 17 Apr 2026 - 2:00

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Inequality homogeneous wave equation

Published on 16 Apr 2026 - 19:36

38

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Convert the eastimate $\|u\|_{L^q(\Bbb{R}^n)}\le \|(\Delta +z) u\|_{L^p}$ into multiplier form

Published on 17 Apr 2026 - 13:29

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Prove $ \|u\|_{L^q(\Bbb{R}^n)}\le \|(\Delta +z) u\|_{L^p(\Bbb{R}^n)} $ when $|z|\le 1$

Published on 17 Apr 2026 - 14:31

List Question

Why is sobolev space $H^m$ embedded in the $C^k$ space?

How to prove that $H^1_{per}$ is an Hilbert space?

function which is not Lipschitz but in $W^{1,\infty}$ on a domain with a slit

Is $H_0^1(\Omega)\subset C(\Omega)?$

Seeking references regarding Zero Extension of Sobolev ($W_0^{1,2}$) functions on a compact domain on $C^\infty$ Riemannian manifold

The Heat Equation in Brezis' book

Question about the decay of $f\in W^{1,2}(\mathbb{R}^2)$

Do $u\in H^1(\Omega)$ and $\Delta u\in L^2(\Omega)$ imply $u\in H^2(\Omega)$?

What do we say about the Stokes Operator $-P \Delta$ on Morrey Spaces?

Weak l.s.c. of $L^2$-norm on $W^{1,2}_0(\Omega)$

Identification of $L^2(0,T;H^2(\Omega))$ with $L^\infty(Q_T)$

inverse laplace operator bounded

Inequality homogeneous wave equation

Convert the eastimate $\|u\|_{L^q(\Bbb{R}^n)}\le \|(\Delta +z) u\|_{L^p}$ into multiplier form

Prove $ \|u\|_{L^q(\Bbb{R}^n)}\le \|(\Delta +z) u\|_{L^p(\Bbb{R}^n)} $ when $|z|\le 1$

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