Question

Potential flow around a torus - Laplace equation in toroidal coordinates

score 1.6k · Answer 1 · 2026-03-24 22:11:45

1.6k

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Potential flow around a torus - Laplace equation in toroidal coordinates

Published on 24 Mar 2026 - 22:11

score 228 · Answer 2 · 2018-04-21 18:40:35

228

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Why does $w=u-h$ satisfy mean value property on any ball inside $B$?

Published on 21 Apr 2018 - 18:40

score 47 · Answer 3 · 2018-04-22 05:04:10

47

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Why does $\underset {x \in \Omega'}{\mathrm {inf}}\ |u_m (x) - u_n (x)| \le \epsilon$?

Published on 22 Apr 2018 - 5:04

score 836 · Answer 4 · 2018-04-22 20:58:02

836

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If $u$ is harmonic then $Du$ is harmonic.

Published on 22 Apr 2018 - 20:58

score 768 · Answer 5 · 2018-04-23 07:40:49

768

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Equivalent definition of subharmonic functions.

Published on 23 Apr 2018 - 7:40

score 433 · Answer 6 · 2026-03-25 01:20:25

433

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Decomposition of a homogeneous polynomial into a sum of harmonic and $x^2 q$.

Published on 25 Mar 2026 - 1:20

score 978 · Answer 7 · 2018-04-24 06:19:46

978

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Harmonic lifts of subharmonic functions are subharmonic.

Published on 24 Apr 2018 - 6:19

score 121 · Answer 8 · 2018-04-24 16:02:52

121

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Why can we asume that $u-v \not \equiv M$ on $\partial B$?

Published on 24 Apr 2018 - 16:02

score 18 · Answer 9 · 2026-03-17 11:01:52

18

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Relationship between arch geometry and undulatory response

Published on 17 Mar 2026 - 11:01

score 141 · Answer 10 · 2026-03-23 08:34:00

141

Views

"Square root" of a decomposition of a homogeneous polynomial to harmonic and $x^2 q$.

Published on 23 Mar 2026 - 8:34

score 174 · Answer 11 · 2018-04-26 17:06:22

174

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If $f\in L^p(\mathbb{R})$ and $h_{\lambda}$ is Poisson Kernel of the upper half plane, then $f*h_{\lambda}(x)$ is harmonic

Published on 26 Apr 2018 - 17:06

score 73 · Answer 12 · 2018-04-28 14:54:14

73

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Proof that $\frac{u_x v_x - u_y v_y}{(u_x^2 + u_y^2)(v_x^2 + v_y^2)}$ is harmonic if $u$ and $v$ are

Published on 28 Apr 2018 - 14:54

score 154 · Answer 13 · 2018-05-02 12:16:44

154

Views

Does a map which preserve harmonic forms preserve co-closedness of forms?

Published on 02 May 2018 - 12:16

score 154 · Answer 14 · 2018-05-02 17:29:03

154

Views

Convergence of harmonic functions

Published on 02 May 2018 - 17:29

score 89 · Answer 15 · 2018-05-04 18:35:44

89

Views

What is the Relationship Between a Sand Pendulum and Infinite Series?

Published on 04 May 2018 - 18:35

List Question

Potential flow around a torus - Laplace equation in toroidal coordinates

Why does $w=u-h$ satisfy mean value property on any ball inside $B$?

Why does $\underset {x \in \Omega'}{\mathrm {inf}}\ |u_m (x) - u_n (x)| \le \epsilon$?

If $u$ is harmonic then $Du$ is harmonic.

Equivalent definition of subharmonic functions.

Decomposition of a homogeneous polynomial into a sum of harmonic and $x^2 q$.

Harmonic lifts of subharmonic functions are subharmonic.

Why can we asume that $u-v \not \equiv M$ on $\partial B$?

Relationship between arch geometry and undulatory response

"Square root" of a decomposition of a homogeneous polynomial to harmonic and $x^2 q$.

If $f\in L^p(\mathbb{R})$ and $h_{\lambda}$ is Poisson Kernel of the upper half plane, then $f*h_{\lambda}(x)$ is harmonic

Proof that $\frac{u_x v_x - u_y v_y}{(u_x^2 + u_y^2)(v_x^2 + v_y^2)}$ is harmonic if $u$ and $v$ are

Does a map which preserve harmonic forms preserve co-closedness of forms?

Convergence of harmonic functions

What is the Relationship Between a Sand Pendulum and Infinite Series?

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