Question

Subharmonic functions problem

score 189 · Answer 1 · 2018-07-02 19:46:15

189

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Subharmonic functions problem

Published on 02 Jul 2018 - 19:46

score 717 · Answer 2 · 2018-07-04 02:38:49

717

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$\Delta^2 (\vert x \vert ^2 u) =0 \;$ for $u \;$ harmonic

Published on 04 Jul 2018 - 2:38

score 35 · Answer 3 · 2018-07-04 22:25:27

35

Views

Is this decreasing in the Harmonic Mean?

Published on 04 Jul 2018 - 22:25

score 318 · Answer 4 · 2018-07-06 00:08:55

318

Views

Maximize the derivative of a bounded harmonic function on the disk

Published on 06 Jul 2018 - 0:08

score 87 · Answer 5 · 2026-03-25 04:39:24

87

Views

Calculating Sobolev norm on boundary by extending the map on M as a harmonic map

Published on 25 Mar 2026 - 4:39

score 402 · Answer 6 · 2018-07-12 23:46:27

402

Views

Singularity in Jensen's Formula Proof

Published on 12 Jul 2018 - 23:46

score 2.3k · Answer 7 · 2018-07-15 14:20:18

2.3k

Views

Does every function has a harmonic conjugate?

Published on 15 Jul 2018 - 14:20

score 1.7k · Answer 8 · 2018-07-16 00:20:29

1.7k

Views

A non-constant harmonic function must have a zero

Published on 16 Jul 2018 - 0:20

score 213 · Answer 9 · 2026-03-25 06:09:01

213

Views

How to complexify a harmonic function with an isolated singularity?

Published on 25 Mar 2026 - 6:09

score 943 · Answer 10 · 2018-07-24 00:33:43

943

Views

Find a conformal map from a half plane deprived of a disk onto an annulus + question on a connected harmonic function

Published on 24 Jul 2018 - 0:33

score 191 · Answer 11 · 2026-03-22 17:01:37

191

Views

Estimating the $L^p$ norm of a second derivative of a solution of the Laplace equation

Published on 22 Mar 2026 - 17:01

score 620 · Answer 12 · 2018-08-01 02:29:40

620

Views

Let $u(z)$ be a harmonic function on $\mathbb{C}$ such that $|u(z)| \leq \sqrt{|z|}$. Show $u$ is constant.

Published on 01 Aug 2018 - 2:29

score 1.6k · Answer 13 · 2018-08-03 03:06:37

1.6k

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$u(x, y) = ax^3 + bxy$, here $a$ and $b$ are real-valued constants. Determine $a$ and $b$ so that the function $u$ is harmonic.

Published on 03 Aug 2018 - 3:06

score 234 · Answer 14 · 2026-03-23 05:04:11

234

Views

Whenever Laplace's equation is solved in $\Omega \subset \mathbb{R}^2$, the boundary $\partial{\Omega}$ is one-dimensional. ...

Published on 23 Mar 2026 - 5:04

score 262 · Answer 15 · 2018-08-05 07:56:28

262

Views

Harmonic function which is zero on the boundary is zero in the domain

Published on 05 Aug 2018 - 7:56

List Question

Subharmonic functions problem

$\Delta^2 (\vert x \vert ^2 u) =0 \;$ for $u \;$ harmonic

Is this decreasing in the Harmonic Mean?

Maximize the derivative of a bounded harmonic function on the disk

Calculating Sobolev norm on boundary by extending the map on M as a harmonic map

Singularity in Jensen's Formula Proof

Does every function has a harmonic conjugate?

A non-constant harmonic function must have a zero

How to complexify a harmonic function with an isolated singularity?

Find a conformal map from a half plane deprived of a disk onto an annulus + question on a connected harmonic function

Estimating the $L^p$ norm of a second derivative of a solution of the Laplace equation

Let $u(z)$ be a harmonic function on $\mathbb{C}$ such that $|u(z)| \leq \sqrt{|z|}$. Show $u$ is constant.

$u(x, y) = ax^3 + bxy$, here $a$ and $b$ are real-valued constants. Determine $a$ and $b$ so that the function $u$ is harmonic.

Whenever Laplace's equation is solved in $\Omega \subset \mathbb{R}^2$, the boundary $\partial{\Omega}$ is one-dimensional. ...

Harmonic function which is zero on the boundary is zero in the domain

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