List questions from harmonic-functions

Published on 11 Mar 2024 - 2:20

47

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Global $L^{2}$ solution of Laplace equation in $\mathbb{R}^{3}$.

Published on 27 Mar 2026 - 0:58

57

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Sum of squares of sines (Normal modes of a harmonic chain) of different periods

Published on 12 Mar 2024 - 8:00

49

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Conormal Derivative and Green Function in integral

Published on 27 Mar 2026 - 16:46

62

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Proving nonexistence of local extrema of harmonic functions using Hessian

Published on 29 Mar 2026 - 18:14

36

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Possible to have only zero eigenvalues of the Hessian of a harmonic function that is neither of the form $ax+by+cz+d$ nor a constant?

Published on 29 Mar 2026 - 18:15

50

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A mathematical statement about Laplace's equation from famous physicist Landau's book

Published on 20 Mar 2024 - 7:53

32

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Finding the harmonic conjugate of the function

Published on 23 Mar 2024 - 19:01

1.9k

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Limit of bounded harmonic functions is harmonic

Published on 06 Jan 2015 - 20:25

60

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Holomorphic function locally represented as $(\partial_{x} - i \partial_{y}) h(x, y)$, with $h$ a scalar harmonic function

Published on 08 Jan 2015 - 12:53

249

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Proving $u(x) = \frac{1}{\omega_n r^{n-1}}\int_{\partial B(x,r)} u\, d\sigma = \frac{n}{\omega_n r^n}\int_{B (x,r)} u\, dV$ for harmonic $u$

Published on 10 Jan 2015 - 16:26

187

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Solving Laplace equation in polar coordinates

Published on 13 Jan 2015 - 15:50

164

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Harmonic maps and angle preservation

Published on 29 Mar 2026 - 11:20

117

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Poisson problem, green's function

Published on 26 Mar 2026 - 17:52

920

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Green's function for Dirichlet problem on a half disk

Published on 20 Jan 2015 - 12:41

List Question

mean value property for subharmonic functions (probabilistic proof)

Global $L^{2}$ solution of Laplace equation in $\mathbb{R}^{3}$.

Sum of squares of sines (Normal modes of a harmonic chain) of different periods

Conormal Derivative and Green Function in integral

Proving nonexistence of local extrema of harmonic functions using Hessian

Possible to have only zero eigenvalues of the Hessian of a harmonic function that is neither of the form $ax+by+cz+d$ nor a constant?

A mathematical statement about Laplace's equation from famous physicist Landau's book

Finding the harmonic conjugate of the function

Limit of bounded harmonic functions is harmonic

Holomorphic function locally represented as $(\partial_{x} - i \partial_{y}) h(x, y)$, with $h$ a scalar harmonic function

Proving $u(x) = \frac{1}{\omega_n r^{n-1}}\int_{\partial B(x,r)} u\, d\sigma = \frac{n}{\omega_n r^n}\int_{B (x,r)} u\, dV$ for harmonic $u$

Solving Laplace equation in polar coordinates

Harmonic maps and angle preservation

Poisson problem, green's function

Green's function for Dirichlet problem on a half disk

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