Question

Harmonic(?) sine and its abbreviation

score 51 · Answer 1 · 2019-08-20 14:42:01

51

Views

Harmonic(?) sine and its abbreviation

Published on 20 Aug 2019 - 14:42

score 174 · Answer 2 · 2019-08-30 21:03:02

174

Views

Let $u \in C^3(\mathbb{R}^n)$ and harmonic such that $u(x) = o(|x|)$ when $|x| \rightarrow \infty$. Show that $\nabla u(0) = 0$ and u is constant

Published on 30 Aug 2019 - 21:03

score 113 · Answer 3 · 2026-03-26 16:56:42

113

Views

show that $f(r) = \frac{1}{\mathrm{area}(S_r)} \int_{S_r} u^2 dS$ is increasing, when $u$ is harmonic

Published on 26 Mar 2026 - 16:56

score 226 · Answer 4 · 2019-09-01 12:12:58

226

Views

If $u$ is harmonic then for $r_1 < r_2$ $ \frac{1}{\text{area}(S_{r1})} \int_{S_{r1}} u^2 dS \le \frac{1}{\text{area}(S_{r2})} \int_{S_{r2}} u^2 dS$

Published on 01 Sep 2019 - 12:12

score 73 · Answer 5 · 2026-03-25 16:05:21

73

Views

Subharmonic functions inequality

Published on 25 Mar 2026 - 16:05

score 201 · Answer 6 · 2026-03-25 12:52:13

201

Views

Is the Dirichlet boundary condition continuous?

Published on 25 Mar 2026 - 12:52

score 359 · Answer 7 · 2019-09-09 22:57:04

359

Views

If $f$ is a holomorphic function then $|f|$ is strictly sub-harmonic.

Published on 09 Sep 2019 - 22:57

score 237 · Answer 8 · 2019-09-11 02:06:38

237

Views

Harmonic circle-valued maps

Published on 11 Sep 2019 - 2:06

score 136 · Answer 9 · 2019-09-14 20:27:43

136

Views

Continuous in punctured ball, bounded implies can be continuously extended?

Published on 14 Sep 2019 - 20:27

score 598 · Answer 10 · 2019-09-15 02:05:26

598

Views

Harmonic in punctured ball and bounded implies harmonic in ball.

Published on 15 Sep 2019 - 2:05

score 833 · Answer 11 · 2019-09-17 22:00:23

833

Views

Laplace equation on the upper half plane with boundary conditions along x=0

Published on 17 Sep 2019 - 22:00

score 104 · Answer 12 · 2026-03-25 20:09:44

104

Views

$\Delta u = 1$ and $u$ convex $\implies$ $u$ quadratic polynomial

Published on 25 Mar 2026 - 20:09

score 171 · Answer 13 · 2019-09-26 18:08:03

171

Views

Show that $u(z)=\frac{1-|z|^2}{|1-z|^2}$ is harmonic in the open disc with center 0 and radius 1

Published on 26 Sep 2019 - 18:08

score 208 · Answer 14 · 2026-03-25 20:12:48

208

Views

How to show a harmonic function is a polynomial?

Published on 25 Mar 2026 - 20:12

score 284 · Answer 15 · 2026-03-25 17:42:06

284

Views

How to compute $\int_0^1\left(\operatorname{Li}_2(x)-\zeta(2)\right)\frac{\ln^2(1-x^2)}{1-x^2}\ dx$

Published on 25 Mar 2026 - 17:42

List Question

Harmonic(?) sine and its abbreviation

Let $u \in C^3(\mathbb{R}^n)$ and harmonic such that $u(x) = o(|x|)$ when $|x| \rightarrow \infty$. Show that $\nabla u(0) = 0$ and u is constant

show that $f(r) = \frac{1}{\mathrm{area}(S_r)} \int_{S_r} u^2 dS$ is increasing, when $u$ is harmonic

If $u$ is harmonic then for $r_1 < r_2$ $ \frac{1}{\text{area}(S_{r1})} \int_{S_{r1}} u^2 dS \le \frac{1}{\text{area}(S_{r2})} \int_{S_{r2}} u^2 dS$

Subharmonic functions inequality

Is the Dirichlet boundary condition continuous?

If $f$ is a holomorphic function then $|f|$ is strictly sub-harmonic.

Harmonic circle-valued maps

Continuous in punctured ball, bounded implies can be continuously extended?

Harmonic in punctured ball and bounded implies harmonic in ball.

Laplace equation on the upper half plane with boundary conditions along x=0

$\Delta u = 1$ and $u$ convex $\implies$ $u$ quadratic polynomial

Show that $u(z)=\frac{1-|z|^2}{|1-z|^2}$ is harmonic in the open disc with center 0 and radius 1

How to show a harmonic function is a polynomial?

How to compute $\int_0^1\left(\operatorname{Li}_2(x)-\zeta(2)\right)\frac{\ln^2(1-x^2)}{1-x^2}\ dx$

Trending Questions

Popular # Hahtags

Popular Questions