Question

Do the level sets of a subharmonic function have measure zero?

score 482 · Answer 1 · 2017-03-27 18:52:42

482

Views

Do the level sets of a subharmonic function have measure zero?

Published on 27 Mar 2017 - 18:52

score 707 · Answer 2 · 2017-03-29 13:55:15

707

Views

Show that if $u$ is non-negative and harmonic then $|\nabla u(x_0)| \leq \frac{2}{R}u(x_0)$

Published on 29 Mar 2017 - 13:55

score 257 · Answer 3 · 2017-03-29 14:48:20

257

Views

Harmonic function with mean value property related to proof of Schwarz's integral formula

Published on 29 Mar 2017 - 14:48

score 78 · Answer 4 · 2017-03-31 16:05:05

78

Views

Numerical solution of Laplace equation on an image

Published on 31 Mar 2017 - 16:05

score 513 · Answer 5 · 2017-03-31 17:41:59

513

Views

subharmonic on punctured disk but extends continuously to origin

Published on 31 Mar 2017 - 17:41

score 60 · Answer 6 · 2026-03-25 13:55:09

60

Views

Harmonic nesting: How often nodes of different sin waves line up with each other?

Published on 25 Mar 2026 - 13:55

score 3.3k · Answer 7 · 2017-04-02 22:34:16

3.3k

Views

Solving Laplace's equation on the circle

Published on 02 Apr 2017 - 22:34

score 620 · Answer 8 · 2017-04-03 16:46:35

620

Views

Solution to Laplace's equation on the circle $0<r<1$

Published on 03 Apr 2017 - 16:46

score 705 · Answer 9 · 2017-04-05 05:44:05

705

Views

Is there an irreducible Markov chain admitting a non-constant bounded harmonic function?

Published on 05 Apr 2017 - 5:44

score 139 · Answer 10 · 2017-04-06 17:48:03

139

Views

Integral involving directional derivative of solution to Laplace's equation

Published on 06 Apr 2017 - 17:48

score 354 · Answer 11 · 2017-04-07 02:13:36

354

Views

Poincaré versus Helmholtz

Published on 07 Apr 2017 - 2:13

score 331 · Answer 12 · 2017-04-07 09:43:26

331

Views

Is the scalar product of the gradient of two harmonic functions an harmonic function?

Published on 07 Apr 2017 - 9:43

score 74 · Answer 13 · 2026-03-29 15:33:22

74

Views

Show that $\int_S|\nabla w|^2 \operatorname{dA}\ge\int_S|\nabla u|^2 \operatorname{dA}$

Published on 29 Mar 2026 - 15:33

score 63 · Answer 14 · 2026-03-29 18:33:35

63

Views

Show that $\int^1_0\left(r\left(\frac{dg}{dr}\right)^2+\frac{g^2}r\right) \operatorname{dr}\ge1$ for any differentiable function $g(r)$.

Published on 29 Mar 2026 - 18:33

score 115 · Answer 15 · 2017-04-09 11:44:34

115

Views

A real function compose a harmonic function is harmonic iff it is linear

Published on 09 Apr 2017 - 11:44

List Question

Do the level sets of a subharmonic function have measure zero?

Show that if $u$ is non-negative and harmonic then $|\nabla u(x_0)| \leq \frac{2}{R}u(x_0)$

Harmonic function with mean value property related to proof of Schwarz's integral formula

Numerical solution of Laplace equation on an image

subharmonic on punctured disk but extends continuously to origin

Harmonic nesting: How often nodes of different sin waves line up with each other?

Solving Laplace's equation on the circle

Solution to Laplace's equation on the circle $0<r<1$

Is there an irreducible Markov chain admitting a non-constant bounded harmonic function?

Integral involving directional derivative of solution to Laplace's equation

Poincaré versus Helmholtz

Is the scalar product of the gradient of two harmonic functions an harmonic function?

Show that $\int_S|\nabla w|^2 \operatorname{dA}\ge\int_S|\nabla u|^2 \operatorname{dA}$

Show that $\int^1_0\left(r\left(\frac{dg}{dr}\right)^2+\frac{g^2}r\right) \operatorname{dr}\ge1$ for any differentiable function $g(r)$.

A real function compose a harmonic function is harmonic iff it is linear

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