List questions from harmonic-functions

Published on 25 Mar 2026 - 16:02

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Does this Laplace equation with 2 initial conditions have separable solutions? How about nonseparable?

Published on 09 Dec 2019 - 15:13

383

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Laplace equation with periodic and mixed boundary conditions

Published on 13 Dec 2019 - 10:02

2.5k

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If $u$ is harmonic then $u^2$ is harmonic?

Published on 17 Dec 2019 - 2:54

1.7k

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If $u(x,y)$ and $v(x,y)$ are harmonic on a domain D, show that $f(z) = (U_y - V_x) + i(U_x + V_y)$ is analytic in D.

Published on 26 Mar 2026 - 17:33

821

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Proof that the sum of the reciprocals of primes diverges

Published on 31 Dec 2019 - 9:38

120

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Laplace equation in the whole space

Published on 25 Mar 2026 - 19:03

52

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Mean value property for 'almost' harmonic function

Published on 11 Jan 2020 - 10:44

41

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Techniques for studying harmonic functions in dimension $ > 2$

Published on 14 Jan 2020 - 12:09

169

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Why is the Laplacian of $|f(x+iy)|^2$ equal to $4|′()|^2$?

Published on 20 Jan 2020 - 21:52

34

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Why does the solution of this Laplace Equation need to be of the form $\sum_{n\geq 1} \sin{nx} [A_n \sinh{(ny)} + B_n \sinh{(n(y- \pi))}]$?

Published on 25 Jan 2020 - 18:31

50

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Mean-value property of harmonic functions using the solution to the Dirichlet problem

Published on 28 Jan 2020 - 2:42

163

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Operator norm of matrix with holomorphic entries is subharmonic

Published on 30 Jan 2020 - 20:52

248

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Subharmonicity implies mean-value inequality

Published on 04 Feb 2020 - 4:54

103

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Compute$\int_0^{2\pi}\frac{\cos^2\theta }{ |re^{i\theta} -z|^2}d\theta$

Published on 04 Feb 2020 - 17:08

List Question

Is there a free-boundary elliptic estimate in $L^p$?

Does this Laplace equation with 2 initial conditions have separable solutions? How about nonseparable?

Laplace equation with periodic and mixed boundary conditions

If $u$ is harmonic then $u^2$ is harmonic?

If $u(x,y)$ and $v(x,y)$ are harmonic on a domain D, show that $f(z) = (U_y - V_x) + i(U_x + V_y)$ is analytic in D.

Proof that the sum of the reciprocals of primes diverges

Laplace equation in the whole space

Mean value property for 'almost' harmonic function

Techniques for studying harmonic functions in dimension $ > 2$

Why is the Laplacian of $|f(x+iy)|^2$ equal to $4|′()|^2$?

Why does the solution of this Laplace Equation need to be of the form $\sum_{n\geq 1} \sin{nx} [A_n \sinh{(ny)} + B_n \sinh{(n(y- \pi))}]$?

Mean-value property of harmonic functions using the solution to the Dirichlet problem

Operator norm of matrix with holomorphic entries is subharmonic

Subharmonicity implies mean-value inequality

Compute$\int_0^{2\pi}\frac{\cos^2\theta }{ |re^{i\theta} -z|^2}d\theta$

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