Question

Equivalent definitions of subharmonicity (Mean Value Inequality vs Viscosity vs Classic)

score 398 · Answer 1 · 2026-03-28 09:45:33

398

Views

Equivalent definitions of subharmonicity (Mean Value Inequality vs Viscosity vs Classic)

Published on 28 Mar 2026 - 9:45

score 225 · Answer 2 · 2020-12-14 05:13:09

225

Views

If $u$ is harmonic in $B(0,1)\subset\mathbb R^2$ with $\vert u\vert\leq1,$ then $\vert\nabla u(0)\vert\leq4/\pi$

Published on 14 Dec 2020 - 5:13

score 27 · Answer 3 · 2026-03-29 17:25:13

27

Views

How to find the complex function corresponding to a potential function?

Published on 29 Mar 2026 - 17:25

score 78 · Answer 4 · 2020-12-14 20:27:06

78

Views

Given a smooth function, does there exist a (semi-)Riemannian metric for which it is harmonic?

Published on 14 Dec 2020 - 20:27

score 92 · Answer 5 · 2020-12-16 10:36:16

92

Views

Given a function $f(z)$ that is analytic over the whole complex plane and Im($f$) $\leq 0$, show that $f$ is constant

Published on 16 Dec 2020 - 10:36

score 601 · Answer 6 · 2020-12-16 13:40:30

601

Views

Gradient estimate for harmonic functions - Isn't a power missing on $N$?

Published on 16 Dec 2020 - 13:40

score 55 · Answer 7 · 2020-12-17 07:35:32

55

Views

Growth Rate of Integral of Harmonic functions

Published on 17 Dec 2020 - 7:35

score 212 · Answer 8 · 2020-12-17 09:51:44

212

Views

If $u(z)$ is non-constant and harmomic in the plane, then show that $u(z)$ comes arbitrarily close to every real value

Published on 17 Dec 2020 - 9:51

score 120 · Answer 9 · 2020-12-17 10:07:03

120

Views

How to use mean value theorem For harmonic functions to prove this

Published on 17 Dec 2020 - 10:07

score 313 · Answer 10 · 2020-12-17 13:33:52

313

Views

How to prove $\int_{0}^{2\pi } \frac{ \sin(\theta - \phi) } { R^2 - 2rR \cos(\theta -\phi) +r^2 } d{\phi} =0$

Published on 17 Dec 2020 - 13:33

score 39 · Answer 11 · 2020-12-17 13:56:30

Proving this result for harmonic function for $|z|>R$ which is similar to Integral formula for harmonic functions in the disc $|z|<R$.

score 25 · Answer 12 · 2020-12-17 16:04:43

25

Views

How to construct such a harmonic function

Published on 17 Dec 2020 - 16:04

score 294 · Answer 13 · 2026-03-26 20:36:33

294

Views

Solid harmonic addition theorem in higher dimensions?

Published on 26 Mar 2026 - 20:36

score 551 · Answer 14 · 2020-12-20 17:21:44

551

Views

Find all entire functions $f$ such that $|f|$ is harmonic.

Published on 20 Dec 2020 - 17:21

score 81 · Answer 15 · 2026-03-27 07:14:55

81

Views

change of variable to get a quasi-cartesian laplace equation?

Published on 27 Mar 2026 - 7:14

List Question

Equivalent definitions of subharmonicity (Mean Value Inequality vs Viscosity vs Classic)

If $u$ is harmonic in $B(0,1)\subset\mathbb R^2$ with $\vert u\vert\leq1,$ then $\vert\nabla u(0)\vert\leq4/\pi$

How to find the complex function corresponding to a potential function?

Given a smooth function, does there exist a (semi-)Riemannian metric for which it is harmonic?

Given a function $f(z)$ that is analytic over the whole complex plane and Im($f$) $\leq 0$, show that $f$ is constant

Gradient estimate for harmonic functions - Isn't a power missing on $N$?

Growth Rate of Integral of Harmonic functions

If $u(z)$ is non-constant and harmomic in the plane, then show that $u(z)$ comes arbitrarily close to every real value

How to use mean value theorem For harmonic functions to prove this

How to prove $\int_{0}^{2\pi } \frac{ \sin(\theta - \phi) } { R^2 - 2rR \cos(\theta -\phi) +r^2 } d{\phi} =0$

Proving this result for harmonic function for $|z|>R$ which is similar to Integral formula for harmonic functions in the disc $|z|<R$.

How to construct such a harmonic function

Solid harmonic addition theorem in higher dimensions?

Find all entire functions $f$ such that $|f|$ is harmonic.

change of variable to get a quasi-cartesian laplace equation?

Trending Questions

Popular # Hahtags

Popular Questions