List questions from harmonic-functions

Published on 25 Mar 2026 - 18:44

91

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Sturm-Liouville equation of a particular solution to the Laplace Equation

Published on 28 Mar 2026 - 16:29

36

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Let $f \in C^2(\mathbb{R}^n)$ harmonic and $g(x):=tan(f(x))+e^{-|x|^2}$ bounded

Published on 09 Apr 2023 - 22:53

58

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Showing that a function is not harmonic

Published on 09 Apr 2023 - 23:35

140

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Exercise regarding the mean value theorem for harmonic functions

Published on 10 Apr 2023 - 20:11

25

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How to determine two functions from an equation relating their Fourier series coefficients

Published on 27 Mar 2026 - 4:21

54

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Show that a solution of the wave equation is time independent

Published on 30 Mar 2026 - 0:21

383

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Minimizing Dirichlet Energy with Constraints

Published on 13 Apr 2023 - 8:11

109

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Solving Laplace's equation using mean value property

Published on 14 Apr 2023 - 14:23

66

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Show that a harmonic function is a polynomial.

Published on 14 Apr 2023 - 21:38

32

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L2 norm of homogeneous harmonic polynomial

Published on 16 Apr 2023 - 7:06

36

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Find all $f\in{C}^2(\mathbb{R})$ such that $(x,y)\rightarrow{f}(x+y)$ is subharmonic.

Published on 17 Apr 2023 - 14:38

78

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Solving the laplacian over a square

Published on 17 Apr 2023 - 19:57

81

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How to prove that $|x|^{2}\Delta f+Cf=0$ implies $f=0$ on $\mathbb{R}^{n}$.

Published on 30 Mar 2026 - 3:03

224

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If u is a positive harmonic function on U, the open unit disc, such that u(0)=1. Find the upper and lower bounds for u(1/2).

Published on 23 Apr 2023 - 16:33

List Question

Generalization for a result on vector analysis

Sturm-Liouville equation of a particular solution to the Laplace Equation

Let $f \in C^2(\mathbb{R}^n)$ harmonic and $g(x):=tan(f(x))+e^{-|x|^2}$ bounded

Showing that a function is not harmonic

Exercise regarding the mean value theorem for harmonic functions

How to determine two functions from an equation relating their Fourier series coefficients

Show that a solution of the wave equation is time independent

Minimizing Dirichlet Energy with Constraints

Solving Laplace's equation using mean value property

Show that a harmonic function is a polynomial.

L2 norm of homogeneous harmonic polynomial

Find all $f\in{C}^2(\mathbb{R})$ such that $(x,y)\rightarrow{f}(x+y)$ is subharmonic.

Solving the laplacian over a square

How to prove that $|x|^{2}\Delta f+Cf=0$ implies $f=0$ on $\mathbb{R}^{n}$.

If u is a positive harmonic function on U, the open unit disc, such that u(0)=1. Find the upper and lower bounds for u(1/2).

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