Question

Determining if a Continuous $u:\mathbb{C}\to \mathbb{R}$ Satisfying some Property is Harmonic

score 103 · Answer 1 · 2015-02-14 12:06:33

Determining if a Continuous $u:\mathbb{C}\to \mathbb{R}$ Satisfying some Property is Harmonic

Published on 14 Feb 2015 - 12:06

score 58 · Answer 2 · 2015-02-16 19:47:46

By direct computation, check that the function u(x) = $|x|^{1/2}$ cos($\theta$/2) is harmonic in the upper half plane H := {x = (x1, x2) | x2 > 0}.

score 64 · Answer 3 · 2015-02-19 01:28:24

64

Views

Must a function hold true for all (x,y) to be harmonic?

Published on 19 Feb 2015 - 1:28

score 270 · Answer 4 · 2015-02-19 21:04:44

270

Views

Source of the "$\cosh$ trick" for Laplacian eigenfunctions or Helmholtz equation solutions?

Published on 19 Feb 2015 - 21:04

score 68 · Answer 5 · 2015-02-24 02:38:02

68

Views

Show an equation only has harmonic solution

Published on 24 Feb 2015 - 2:38

score 129 · Answer 6 · 2015-03-02 00:08:06

129

Views

How can I prove that $\partial\varphi\neq0$ implies $\bar\partial\partial\varphi>0$?

Published on 02 Mar 2015 - 0:08

score 696 · Answer 7 · 2026-03-30 16:44:13

696

Views

How to check the barrier function is superharmonic?

Published on 30 Mar 2026 - 16:44

score 149 · Answer 8 · 2015-03-09 05:18:35

149

Views

Compact set of measure zero and sequence of Harmonic Functions with nice properties.

Published on 09 Mar 2015 - 5:18

score 4.3k · Answer 9 · 2026-03-30 16:41:43

4.3k

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Subharmonic function equivalent non-negative laplacian

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score 705 · Answer 10 · 2015-03-18 10:40:42

705

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Prove the Inverse of a Nonconstant Harmonic Function is Unbounded

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score 795 · Answer 11 · 2015-03-19 15:12:50

795

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Can Laplace's equation be solved in a domain that is not simply connected?

Published on 19 Mar 2015 - 15:12

score 2k · Answer 12 · 2015-03-21 02:36:39

2k

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Gradient of Harmonic Function

Published on 21 Mar 2015 - 2:36

score 2.8k · Answer 13 · 2015-03-25 13:02:48

2.8k

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Zeros of a harmonic function

Published on 25 Mar 2015 - 13:02

score 801 · Answer 14 · 2015-03-29 00:38:35

801

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Average Property of Harmonic Function

Published on 29 Mar 2015 - 0:38

score 74 · Answer 15 · 2015-03-31 16:25:33

74

Views

Find a complex-differentiable function with real part $x^2(ay+8) +4y^2(y+b)$

Published on 31 Mar 2015 - 16:25

List Question

Determining if a Continuous $u:\mathbb{C}\to \mathbb{R}$ Satisfying some Property is Harmonic

By direct computation, check that the function u(x) = $|x|^{1/2}$ cos($\theta$/2) is harmonic in the upper half plane H := {x = (x1, x2) | x2 > 0}.

Must a function hold true for all (x,y) to be harmonic?

Source of the "$\cosh$ trick" for Laplacian eigenfunctions or Helmholtz equation solutions?

Show an equation only has harmonic solution

How can I prove that $\partial\varphi\neq0$ implies $\bar\partial\partial\varphi>0$?

How to check the barrier function is superharmonic?

Compact set of measure zero and sequence of Harmonic Functions with nice properties.

Subharmonic function equivalent non-negative laplacian

Prove the Inverse of a Nonconstant Harmonic Function is Unbounded

Can Laplace's equation be solved in a domain that is not simply connected?

Gradient of Harmonic Function

Zeros of a harmonic function

Average Property of Harmonic Function

Find a complex-differentiable function with real part $x^2(ay+8) +4y^2(y+b)$

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