List questions from harmonic-functions

Published on 03 May 2021 - 5:20

60

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$u$ harmonic and $\lim_{|z| \to \infty} u(z) = 0$ imply that $u \equiv 0$ in $\mathbb{C}$.

Published on 04 May 2021 - 22:38

74

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How to prove $(\frac1\pi)\int_{-\pi}^\pi \left(\frac {1-r^2}{1-2r\cos\theta+r^2}\right)^2d\theta = \frac {2(1+r^2)}{1-r^2}$?

Published on 05 May 2021 - 1:34

123

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How to calculate the volume of the intersection of two spheres of same radius in $\Bbb {R}^n$?

Published on 02 Apr 2026 - 3:17

59

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Is there any counter example for an unbounded function which satisfy this restricted 'MVP'?

Published on 01 Apr 2026 - 22:06

116

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Laplace's Equation looking for vertical displacement of a membrane

Published on 13 May 2021 - 14:12

30

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Boundary characterization of harmonic functions on $\Bbb R^n$

Published on 29 Mar 2026 - 19:16

218

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Show that a multivariate polynomial is identically zero.

Published on 16 May 2021 - 18:27

138

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Helmholtz equation for gabriel's horn

Published on 01 Apr 2026 - 21:00

102

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Help finding mistake in argument about Poisson integrals

Published on 25 May 2021 - 22:50

177

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Why is the (Laplace) E (x) / second derivative equal to 0 of a Newton Potential?

Published on 26 May 2021 - 21:17

222

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Evaluation of Poisson Kernel in the upper half space ($n$-dimensions)

Published on 27 May 2021 - 3:11

97

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Conductive ball submerged in electric field

Published on 29 May 2021 - 22:01

164

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A harmonic function is non-decreasing

Published on 24 Feb 2026 - 13:41

86

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How to show function represent angle of triangle is harmonic

Published on 08 Jun 2021 - 17:51

List Question

Sufficient conditions for being a harmonic function

$u$ harmonic and $\lim_{|z| \to \infty} u(z) = 0$ imply that $u \equiv 0$ in $\mathbb{C}$.

How to prove $(\frac1\pi)\int_{-\pi}^\pi \left(\frac {1-r^2}{1-2r\cos\theta+r^2}\right)^2d\theta = \frac {2(1+r^2)}{1-r^2}$?

How to calculate the volume of the intersection of two spheres of same radius in $\Bbb {R}^n$?

Is there any counter example for an unbounded function which satisfy this restricted 'MVP'?

Laplace's Equation looking for vertical displacement of a membrane

Boundary characterization of harmonic functions on $\Bbb R^n$

Show that a multivariate polynomial is identically zero.

Helmholtz equation for gabriel's horn

Help finding mistake in argument about Poisson integrals

Why is the (Laplace) E (x) / second derivative equal to 0 of a Newton Potential?

Evaluation of Poisson Kernel in the upper half space ($n$-dimensions)

Conductive ball submerged in electric field

A harmonic function is non-decreasing

How to show function represent angle of triangle is harmonic

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