Question

Potential flow around a torus - Laplace equation in toroidal coordinates

score 1.6k · Answer 1 · 2026-05-10 13:48:39

1.6k

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Potential flow around a torus - Laplace equation in toroidal coordinates

Published on 10 May 2026 - 13:48

score 231 · Answer 2 · 2026-04-13 07:32:23

231

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

Published on 13 Apr 2026 - 7:32

score 50 · Answer 3 · 2026-04-16 14:53:13

50

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

Published on 16 Apr 2026 - 14:53

score 839 · Answer 4 · 2026-04-15 05:09:31

839

Views

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

Published on 15 Apr 2026 - 5:09

score 771 · Answer 5 · 2026-04-12 07:53:49

771

Views

Equivalent definition of subharmonic functions.

Published on 12 Apr 2026 - 7:53

score 435 · Answer 6 · 2026-04-15 08:43:56

435

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

Published on 15 Apr 2026 - 8:43

score 981 · Answer 7 · 2026-04-10 23:29:41

981

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Harmonic lifts of subharmonic functions are subharmonic.

Published on 10 Apr 2026 - 23:29

score 124 · Answer 8 · 2026-04-15 19:15:57

124

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

Published on 15 Apr 2026 - 19:15

score 21 · Answer 9 · 2026-05-10 14:54:13

21

Views

Relationship between arch geometry and undulatory response

Published on 10 May 2026 - 14:54

score 149 · Answer 10 · 2026-04-29 12:19:21

149

Views

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

Published on 29 Apr 2026 - 12:19

score 177 · Answer 11 · 2026-04-15 11:15:55

177

Views

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 15 Apr 2026 - 11:15

score 76 · Answer 12 · 2026-04-15 13:37:26

76

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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 15 Apr 2026 - 13:37

score 156 · Answer 13 · 2026-04-10 22:39:48

156

Views

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

Published on 10 Apr 2026 - 22:39

score 158 · Answer 14 · 2026-04-11 04:57:20

158

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Convergence of harmonic functions

Published on 11 Apr 2026 - 4:57

score 92 · Answer 15 · 2026-04-10 11:40:18

92

Views

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

Published on 10 Apr 2026 - 11:40

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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