Question

Laplace's equation on the plane: how much boundary data must be specified to guarantee existence and uniqueness?

score 140 · Answer 1 · 2021-03-06 13:53:24

140

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Laplace's equation on the plane: how much boundary data must be specified to guarantee existence and uniqueness?

Published on 06 Mar 2021 - 13:53

score 149 · Answer 2 · 2026-04-01 18:53:35

149

Views

Can I use the mean value property for a function that is harmonic on only the interior of a ball?

Published on 01 Apr 2026 - 18:53

score 75 · Answer 3 · 2021-03-10 18:47:33

75

Views

Prove: $\sum\limits_{j=1}^{2^n}\frac{1}{j} \geq 1 + \frac{n}{2}$ for all positive integers $n$.

Published on 10 Mar 2021 - 18:47

score 421 · Answer 4 · 2026-03-26 20:38:48

421

Views

Fourier Transform of a harmonic polynomial

Published on 26 Mar 2026 - 20:38

score 51 · Answer 5 · 2021-03-12 16:04:04

51

Views

Holomorphicity of $\sin(\theta)\cos(\theta)+i\cos(\theta)^2$ imply that $\theta$ is constant

Published on 12 Mar 2021 - 16:04

score 262 · Answer 6 · 2021-03-14 23:32:34

262

Views

Harmonic function such that $u =\partial_\nu u = 0$ on a surface must vanish.

Published on 14 Mar 2021 - 23:32

score 395 · Answer 7 · 2026-03-28 22:24:52

395

Views

Show that a continuous weakly harmonic function is harmonic.

Published on 28 Mar 2026 - 22:24

score 26 · Answer 8 · 2021-03-17 19:29:26

Does there exist a 2D harmonic function which never goes to ∞ at any point, goes to 0 as r goes to ∞, and isn't f=0?

score 371 · Answer 9 · 2021-03-21 21:00:36

371

Views

Is it true that a smooth, harmonic functions with compactly supported gradient is trivial?

Published on 21 Mar 2021 - 21:00

score 84 · Answer 10 · 2021-03-23 04:06:41

84

Views

non-constant harmonic function on simply connected domain does not achieve maximum in the interior of the domain

Published on 23 Mar 2021 - 4:06

score 221 · Answer 11 · 2021-03-26 14:37:59

221

Views

Poisson Integral for half plane approaches argument

Published on 26 Mar 2021 - 14:37

score 261 · Answer 12 · 2021-03-28 20:23:26

261

Views

average value of harmonic function around a circle

Published on 28 Mar 2021 - 20:23

score 393 · Answer 13 · 2026-04-01 19:22:08

393

Views

How do derivatives w/r to polar variables behave at the origin?

Published on 01 Apr 2026 - 19:22

score 119 · Answer 14 · 2021-04-01 02:03:49

119

Views

Why does $\partial x/\partial r=x/r$ for $x^2+y^2+z^2=r^2$? (Mean Value Property for Harmonic Functions over the Sphere)

Published on 01 Apr 2021 - 2:03

score 53 · Answer 15 · 2026-03-30 02:05:35

53

Views

How to estimate this trigonometric sum?

Published on 30 Mar 2026 - 2:05

List Question

Laplace's equation on the plane: how much boundary data must be specified to guarantee existence and uniqueness?

Can I use the mean value property for a function that is harmonic on only the interior of a ball?

Prove: $\sum\limits_{j=1}^{2^n}\frac{1}{j} \geq 1 + \frac{n}{2}$ for all positive integers $n$.

Fourier Transform of a harmonic polynomial

Holomorphicity of $\sin(\theta)\cos(\theta)+i\cos(\theta)^2$ imply that $\theta$ is constant

Harmonic function such that $u =\partial_\nu u = 0$ on a surface must vanish.

Show that a continuous weakly harmonic function is harmonic.

Does there exist a 2D harmonic function which never goes to ∞ at any point, goes to 0 as r goes to ∞, and isn't f=0?

Is it true that a smooth, harmonic functions with compactly supported gradient is trivial?

non-constant harmonic function on simply connected domain does not achieve maximum in the interior of the domain

Poisson Integral for half plane approaches argument

average value of harmonic function around a circle

How do derivatives w/r to polar variables behave at the origin?

Why does $\partial x/\partial r=x/r$ for $x^2+y^2+z^2=r^2$? (Mean Value Property for Harmonic Functions over the Sphere)

How to estimate this trigonometric sum?

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