Question

Prove $\int_{\mathbb{R}^N}u^a\nabla u\cdot\nabla\Delta u=C(\int_{\mathbb{R}^N}|D^2 (u^{(a+2)/2})|^2+\int_{\mathbb{R}^N}|\nabla(u^{(a+2)/4})|^4)$

score 135 · Answer 1 · 2026-04-24 01:10:30

135

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Prove $\int_{\mathbb{R}^N}u^a\nabla u\cdot\nabla\Delta u=C(\int_{\mathbb{R}^N}|D^2 (u^{(a+2)/2})|^2+\int_{\mathbb{R}^N}|\nabla(u^{(a+2)/4})|^4)$

Published on 24 Apr 2026 - 1:10

score 2.3k · Answer 2 · 2026-04-15 05:12:25

2.3k

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Find the area under the curve: $r = 2 \sin (3\theta)$

Published on 15 Apr 2026 - 5:12

score 54 · Answer 3 · 2026-04-14 02:12:23

54

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Identify the parametrization

Published on 14 Apr 2026 - 2:12

score 656 · Answer 4 · 2026-04-17 01:17:34

656

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Proof that the hessian matrix of a function is symmetric

Published on 17 Apr 2026 - 1:17

score 45 · Answer 5 · 2026-04-24 01:02:49

45

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score 5.2k · Answer 6 · 2026-04-13 13:08:55

5.2k

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Identify local maximum/minimum from contour map

Published on 13 Apr 2026 - 13:08

score 85 · Answer 7 · 2026-04-11 03:10:24

85

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Finding the critical points of this multivariable function

Published on 11 Apr 2026 - 3:10

score 1.9k · Answer 8 · 2026-04-16 10:54:28

1.9k

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Find the volume bounded by the $xy$ plane, cylinder $x^2 + y^2 = 1$ and sphere $x^2 + y^2 +z^2 = 4$

Published on 16 Apr 2026 - 10:54

score 94 · Answer 9 · 2026-04-10 08:28:01

94

Views

Why is viewing parametric equations in two dimensions better than three dimensions?

Published on 10 Apr 2026 - 8:28

score 113 · Answer 10 · 2026-04-12 15:04:17

113

Views

How to prove that $\vec{x}$ is a local minimum using level curves (if the hessian is inconclusive)?

Published on 12 Apr 2026 - 15:04

score 534 · Answer 11 · 2026-04-17 01:08:34

534

Views

Area between two spirals

Published on 17 Apr 2026 - 1:08

score 423 · Answer 12 · 2026-04-17 03:14:30

423

Views

Why is the dot product of a vector dot a matrix a vector?

Published on 17 Apr 2026 - 3:14

score 65 · Answer 13 · 2026-04-11 06:49:04

65

Views

Multivariable Calculus. Help o how to integrate and To prove a Rotational property

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score 607 · Answer 14 · 2026-04-15 06:21:51

607

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Implication of the Symmetry of the Christoffel Symbol

Published on 15 Apr 2026 - 6:21

score 493 · Answer 15 · 2026-03-24 22:06:50

493

Views

When does differentiation commute with convolution with an approximate identity?

Published on 24 Mar 2026 - 22:06

List Question

Prove $\int_{\mathbb{R}^N}u^a\nabla u\cdot\nabla\Delta u=C(\int_{\mathbb{R}^N}|D^2 (u^{(a+2)/2})|^2+\int_{\mathbb{R}^N}|\nabla(u^{(a+2)/4})|^4)$

Find the area under the curve: $r = 2 \sin (3\theta)$

Identify the parametrization

Proof that the hessian matrix of a function is symmetric

Construct a disproving example to the statement

Identify local maximum/minimum from contour map

Finding the critical points of this multivariable function

Find the volume bounded by the $xy$ plane, cylinder $x^2 + y^2 = 1$ and sphere $x^2 + y^2 +z^2 = 4$

Why is viewing parametric equations in two dimensions better than three dimensions?

How to prove that $\vec{x}$ is a local minimum using level curves (if the hessian is inconclusive)?

Area between two spirals

Why is the dot product of a vector dot a matrix a vector?

Multivariable Calculus. Help o how to integrate and To prove a Rotational property

Implication of the Symmetry of the Christoffel Symbol

When does differentiation commute with convolution with an approximate identity?

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