Question

Decomposition into spherical harmonics

score 202 · Answer 1 · 2026-03-27 05:15:57

Decomposition into spherical harmonics

Published on 27 Mar 2026 - 5:15

score 84 · Answer 2 · 2022-05-01 14:29:58

If $u$ is complex valued and harmonic on a connected open set, and if $u^2$ is harmonic, then either $u$ is holomorphic or $\bar{u}$ is

score 66 · Answer 3 · 2026-04-02 15:51:58

66

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let h be a harmonic function in a simply connected space $D$, prove that there exists an analytic $f=u+iv$ in $D$ s.t $u+v=h$

Published on 02 Apr 2026 - 15:51

score 176 · Answer 4 · 2022-05-05 00:31:04

176

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A boundary value problem of a Harmonic potential

Published on 05 May 2022 - 0:31

score 48 · Answer 5 · 2026-04-07 00:43:54

48

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Applying multivariate chain rule

Published on 07 Apr 2026 - 0:43

score 53 · Answer 6 · 2026-03-27 01:43:10

53

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Spherical harmonics orthogonality

Published on 27 Mar 2026 - 1:43

score 70 · Answer 7 · 2022-05-07 01:48:50

70

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Laplace equation on a rectangle with inhomogeneous boundary conditions

Published on 07 May 2022 - 1:48

score 25 · Answer 8 · 2022-05-13 06:24:35

25

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Find harmonic $u : \mathbb{R}^2 \to \mathbb{R}$ such that $u(x, 0) = u_y(0,0) = 0.$

Published on 13 May 2022 - 6:24

score 49 · Answer 9 · 2026-03-29 10:15:32

49

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Conjugate of the discrete Laplacian Green's function on a square lattice

Published on 29 Mar 2026 - 10:15

score 146 · Answer 10 · 2022-05-17 07:04:34

146

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Prove the constancy of a harmonic function with $\lim_{\vert x\vert\rightarrow\infty}\frac{\vert f(x)\vert}{\ln\vert x\vert}=0$.

Published on 17 May 2022 - 7:04

score 90 · Answer 11 · 2022-05-17 10:33:01

90

Views

Prove the uniqueness of $u\in H_0^1(\Omega)$ with $\Delta u=\vert u\vert^{q-1}u+f$ in $\Omega$ with $\Omega$ as a bounded domain with smooth boundary.

Published on 17 May 2022 - 10:33

score 94 · Answer 12 · 2022-05-22 18:56:35

94

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A sequence of harmonic functions on $\mathbb{R}^{2}$ converging in distribution must necessarily converge locally uniformly to an harmonic function.

Published on 22 May 2022 - 18:56

score 46 · Answer 13 · 2026-03-28 10:35:15

46

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How many positive harmonic functions are there on a half-space for a vanishing boundary condition

Published on 28 Mar 2026 - 10:35

score 42 · Answer 14 · 2022-06-02 18:13:52

42

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Estimate the value of a nonnegative harmonic function

Published on 02 Jun 2022 - 18:13

score 401 · Answer 15 · 2026-03-25 15:45:36

401

Views

Dirichlet Problem on Upper Half Plane using Complex Analysis

Published on 25 Mar 2026 - 15:45

List Question

Decomposition into spherical harmonics

If $u$ is complex valued and harmonic on a connected open set, and if $u^2$ is harmonic, then either $u$ is holomorphic or $\bar{u}$ is

let h be a harmonic function in a simply connected space $D$, prove that there exists an analytic $f=u+iv$ in $D$ s.t $u+v=h$

A boundary value problem of a Harmonic potential

Applying multivariate chain rule

Spherical harmonics orthogonality

Laplace equation on a rectangle with inhomogeneous boundary conditions

Find harmonic $u : \mathbb{R}^2 \to \mathbb{R}$ such that $u(x, 0) = u_y(0,0) = 0.$

Conjugate of the discrete Laplacian Green's function on a square lattice

Prove the constancy of a harmonic function with $\lim_{\vert x\vert\rightarrow\infty}\frac{\vert f(x)\vert}{\ln\vert x\vert}=0$.

Prove the uniqueness of $u\in H_0^1(\Omega)$ with $\Delta u=\vert u\vert^{q-1}u+f$ in $\Omega$ with $\Omega$ as a bounded domain with smooth boundary.

A sequence of harmonic functions on $\mathbb{R}^{2}$ converging in distribution must necessarily converge locally uniformly to an harmonic function.

How many positive harmonic functions are there on a half-space for a vanishing boundary condition

Estimate the value of a nonnegative harmonic function

Dirichlet Problem on Upper Half Plane using Complex Analysis

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