List questions from harmonic-functions

Published on 21 May 2013 - 19:54

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How to solve the two dimensional Laplace's equation for certain cases?

Published on 22 May 2013 - 20:54

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Harmonic functions in $\mathbb{R}^d$

Published on 24 May 2013 - 15:28

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Existence theorem for Laplace's equation.

Published on 25 May 2013 - 12:33

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Constants in Laplace's equation for a cube

Published on 27 May 2013 - 6:41

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Showing that if $u$ is a real-valued harmonic function then for any real $c$ we have that $u^{-1}(c)$ is unbounded

Published on 29 May 2013 - 14:45

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Mean Value Property of Harmonic Functions

Published on 30 May 2013 - 19:50

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Solving Laplace's equation using finite differences

Published on 28 Mar 2026 - 11:52

2.2k

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Proof of weak maximum principle.

Published on 02 Jun 2013 - 23:25

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Why is the harmonic function $ \log(x^2 + y^2) $ not the real part of any function that is analytic in $ \mathbb{C} - \{0\} $?

Published on 12 Jun 2013 - 14:09

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Approximation of a harmonic function on the unit disc by harmonic polynomials.

Published on 12 Jun 2013 - 17:28

1.5k

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Harnack's inequality Evans' PDE book

Published on 13 Jun 2013 - 1:26

1.8k

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Show that a harmonic function $ u(r, \theta) $ dependent only on $ r $ has the form $ u(r, \theta) = a \log r + b $

Published on 13 Jun 2013 - 2:49

3.6k

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Derive the Poisson Formula for a bounded C-harmonic function in the upper half-plane.

Published on 14 Jun 2013 - 10:53

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I have a function $ u(x, y) = \text{Re}(f(z)) $ that is bounded, harmonic on the UHP and continuous on the real axis. How can I show f is bounded?

Published on 15 Jun 2013 - 4:32

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Harmonic Function Transformation Help

How to solve the two dimensional Laplace's equation for certain cases?

Harmonic functions in $\mathbb{R}^d$

Existence theorem for Laplace's equation.

Constants in Laplace's equation for a cube

Showing that if $u$ is a real-valued harmonic function then for any real $c$ we have that $u^{-1}(c)$ is unbounded

Mean Value Property of Harmonic Functions

Solving Laplace's equation using finite differences

Proof of weak maximum principle.

Why is the harmonic function $ \log(x^2 + y^2) $ not the real part of any function that is analytic in $ \mathbb{C} - \{0\} $?

Approximation of a harmonic function on the unit disc by harmonic polynomials.

Harnack's inequality Evans' PDE book

Show that a harmonic function $ u(r, \theta) $ dependent only on $ r $ has the form $ u(r, \theta) = a \log r + b $

Derive the Poisson Formula for a bounded C-harmonic function in the upper half-plane.

I have a function $ u(x, y) = \text{Re}(f(z)) $ that is bounded, harmonic on the UHP and continuous on the real axis. How can I show f is bounded?

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