List questions from harmonic-functions

Published on 10 Jul 2020 - 6:20

181

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Finding the zero set of the gradient of a harmonic function

Published on 11 Jul 2020 - 13:35

76

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$h(x,y)$ harmonic with conjugate harmonic conjugate $g(x,y)$. Show $\log(f(x,y)) = \log(h(x,y)^2 + g(x,y)^2)$ is harmonic in $\mathbb{D}$

Published on 11 Jul 2020 - 23:30

301

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Finding an unbounded harmonic function with prescribed boundary values

Published on 13 Jul 2020 - 6:21

244

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Existence of minimizer of energy

Published on 15 Jul 2020 - 20:48

74

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Harmonic function problem

Published on 25 Mar 2026 - 20:40

44

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Solution verification: Harmonic polynomial $p \in \mathbb{R}[x_1, \dots, x_n]$ divisible by $x_1^2+\dots+x_n^2$ must be identically $0.$

Published on 18 Jul 2020 - 9:00

125

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How can I justify that I can put the laplace operator under the integral?

Published on 25 Mar 2026 - 15:47

38

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Can a unique solution exist for this boundary value problem?

Published on 26 Jul 2020 - 7:55

76

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Easy way to check that real part of $e^{-\frac{1}{z^{4}}}$ is harmonic.

Published on 27 Mar 2026 - 5:39

554

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Integrating spherical harmonic function

Published on 25 Mar 2026 - 17:28

186

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Proof that Harmonic Implies Conformal

Published on 14 Jul 2016 - 1:00

31

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The unique tangent of super-harmonic function on the liminf of the singularity

Published on 14 Jul 2016 - 15:53

506

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Conditions for membership of $H^2$

Published on 27 Mar 2026 - 19:15

25

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Harmonic polymonials approximating function

Published on 16 Jul 2016 - 5:14

List Question

Maximize $u_x(0)$ for a harmonic function $u:D\rightarrow [0,1]$

Finding the zero set of the gradient of a harmonic function

$h(x,y)$ harmonic with conjugate harmonic conjugate $g(x,y)$. Show $\log(f(x,y)) = \log(h(x,y)^2 + g(x,y)^2)$ is harmonic in $\mathbb{D}$

Finding an unbounded harmonic function with prescribed boundary values

Existence of minimizer of energy

Harmonic function problem

Solution verification: Harmonic polynomial $p \in \mathbb{R}[x_1, \dots, x_n]$ divisible by $x_1^2+\dots+x_n^2$ must be identically $0.$

How can I justify that I can put the laplace operator under the integral?

Can a unique solution exist for this boundary value problem?

Easy way to check that real part of $e^{-\frac{1}{z^{4}}}$ is harmonic.

Integrating spherical harmonic function

Proof that Harmonic Implies Conformal

The unique tangent of super-harmonic function on the liminf of the singularity

Conditions for membership of $H^2$

Harmonic polymonials approximating function

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