Question

Poisson kernel equivalence

score 173 · Answer 1 · 2020-05-25 19:47:27

173

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Poisson kernel equivalence

Published on 25 May 2020 - 19:47

score 143 · Answer 2 · 2020-05-25 21:03:54

143

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Intuitive explanation of solution to Laplace's equation on unit disc with boundary conditions (i) $u(1,\theta)=c$, & (ii) $u(1,\theta)=\sin(\theta)$?

Published on 25 May 2020 - 21:03

score 1.8k · Answer 3 · 2026-03-25 23:39:09

1.8k

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Prove that $u(x,y) = \frac{x}{x^2+y^2}$ is harmonic in $\mathbb{R}^2\setminus\{(0,0)\}$

Published on 25 Mar 2026 - 23:39

score 760 · Answer 4 · 2020-05-29 19:13:46

760

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Is it true that $u$ is harmonic if and only if $u$ satisfies the mean value property?

Published on 29 May 2020 - 19:13

score 32 · Answer 5 · 2026-03-25 15:52:34

32

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Where to find reference for the energy method $\lambda u- \Delta u=f(x) \hspace{1cm} x \in \Omega, \hspace{1cm}$

Published on 25 Mar 2026 - 15:52

score 1.1k · Answer 6 · 2026-03-25 22:05:56

1.1k

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Proof of uniqueness of solution of the Poisson's equation for given boundary conditions

Published on 25 Mar 2026 - 22:05

score 533 · Answer 7 · 2020-06-02 12:06:55

533

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Deriving (using Fourier transform) the Poisson kernel for solving the Dirichlet problem on unit balls

Published on 02 Jun 2020 - 12:06

score 45 · Answer 8 · 2026-03-26 01:14:35

45

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Analytic and harmonic functions in the unit disc (Question 4.1.1 of "Complex Polynomials" by Sheil-Small)

Published on 26 Mar 2026 - 1:14

score 166 · Answer 9 · 2026-03-26 06:21:09

166

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If $\Delta \varphi =0$ then $\nabla \times \nabla \varphi =0$.

Published on 26 Mar 2026 - 6:21

score 63 · Answer 10 · 2020-06-05 11:37:21

63

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How to prove this set of functions has only one element

Published on 05 Jun 2020 - 11:37

score 143 · Answer 11 · 2020-06-06 14:14:07

143

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Proof the function is harmonic without differetiation

Published on 06 Jun 2020 - 14:14

score 82 · Answer 12 · 2020-06-07 12:52:32

82

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Laplace Equation on a circular strip

Published on 07 Jun 2020 - 12:52

score 39 · Answer 13 · 2020-06-07 16:02:57

39

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Does the mean value property hold for arbitrary surfaces?

Published on 07 Jun 2020 - 16:02

score 33 · Answer 14 · 2020-06-09 15:42:03

33

Views

How do I reach this harmonic equation?

Published on 09 Jun 2020 - 15:42

score 259 · Answer 15 · 2020-06-09 22:55:47

259

Views

An inequality relating to $L^2$ norms of the gradient of a harmonic polynomial

Published on 09 Jun 2020 - 22:55

List Question

Poisson kernel equivalence

Intuitive explanation of solution to Laplace's equation on unit disc with boundary conditions (i) $u(1,\theta)=c$, & (ii) $u(1,\theta)=\sin(\theta)$?

Prove that $u(x,y) = \frac{x}{x^2+y^2}$ is harmonic in $\mathbb{R}^2\setminus\{(0,0)\}$

Is it true that $u$ is harmonic if and only if $u$ satisfies the mean value property?

Where to find reference for the energy method $\lambda u- \Delta u=f(x) \hspace{1cm} x \in \Omega, \hspace{1cm}$

Proof of uniqueness of solution of the Poisson's equation for given boundary conditions

Deriving (using Fourier transform) the Poisson kernel for solving the Dirichlet problem on unit balls

Analytic and harmonic functions in the unit disc (Question 4.1.1 of "Complex Polynomials" by Sheil-Small)

If $\Delta \varphi =0$ then $\nabla \times \nabla \varphi =0$.

How to prove this set of functions has only one element

Proof the function is harmonic without differetiation

Laplace Equation on a circular strip

Does the mean value property hold for arbitrary surfaces?

How do I reach this harmonic equation?

An inequality relating to $L^2$ norms of the gradient of a harmonic polynomial

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