List questions from harmonic-functions

Published on 07 Apr 2021 - 18:37

392

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$u$ is harmonic, prove that $v(x)=\frac{1}{|x|^{n-2}}\cdot u\left(\frac{x}{|x|^2}\right)$ is harmonic.

Published on 11 Apr 2021 - 9:36

99

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Maximum principle for $\varphi\in C^0(\overline{B},\mathbb{R}^2)\cap C^2(B,\mathbb{R}^2)$

Published on 11 Apr 2021 - 18:01

597

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Show that $H(x):=\frac{1}{|x|^{n-2}}u(\frac{x}{|x|^2})$ is harmonic if $u$ is harmonic

Published on 01 Apr 2026 - 19:20

67

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Classify all harmonic $f$ s.t. $f=gh$

Published on 14 Apr 2021 - 18:59

192

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Double layer potential in 1d?

Published on 29 Mar 2026 - 19:08

39

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Lifting Minimal Surfaces

Published on 26 Mar 2026 - 16:02

86

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Given $u$ harmonic find all matrices $Q$ s.t. $u \circ Q$ harmonic

Published on 20 Apr 2021 - 20:26

101

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Expansion of a function in Spherical Harmonics

Published on 26 Mar 2026 - 20:38

35

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Typo in this proof about harmonic functions?

Published on 02 Apr 2026 - 20:08

83

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Taking limits in a variational PDE with respect to a parameter

Published on 28 Mar 2026 - 11:35

145

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Determine all positive harmonic functions

Published on 29 Apr 2021 - 0:47

152

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show that $u(r e^{i \theta}) = \theta \log r$ is harmonic in $\mathbb{C} \setminus (- \infty , 0]$.

Published on 01 May 2021 - 16:46

87

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show that $u$ is harmonic with a condition

Published on 02 May 2021 - 18:51

140

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Physical Intuition for Mean Value Property of Heat Equation.

Published on 01 Apr 2026 - 14:23

List Question

how can it be proved that $\text{Log}|z-z_0|$ is harmonic in $\mathbb{C}\setminus\{z_0\}$?

$u$ is harmonic, prove that $v(x)=\frac{1}{|x|^{n-2}}\cdot u\left(\frac{x}{|x|^2}\right)$ is harmonic.

Maximum principle for $\varphi\in C^0(\overline{B},\mathbb{R}^2)\cap C^2(B,\mathbb{R}^2)$

Show that $H(x):=\frac{1}{|x|^{n-2}}u(\frac{x}{|x|^2})$ is harmonic if $u$ is harmonic

Classify all harmonic $f$ s.t. $f=gh$

Double layer potential in 1d?

Lifting Minimal Surfaces

Given $u$ harmonic find all matrices $Q$ s.t. $u \circ Q$ harmonic

Expansion of a function in Spherical Harmonics

Typo in this proof about harmonic functions?

Taking limits in a variational PDE with respect to a parameter

Determine all positive harmonic functions

show that $u(r e^{i \theta}) = \theta \log r$ is harmonic in $\mathbb{C} \setminus (- \infty , 0]$.

show that $u$ is harmonic with a condition

Physical Intuition for Mean Value Property of Heat Equation.

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