List questions from potential-theory

Published on 11 Apr 2026 - 12:00

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Why is the integral of $\|\nabla f\|^2$ called the energy of $f$?

Published on 13 Apr 2026 - 19:38

273

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Finding the transfinite diameter of the level sets of complex logarithm

Published on 13 Apr 2026 - 5:19

138

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Show that requiring Electrostatic potential to be a stationary point of Electrostatic potential energy is equivalent to Laplace's equation.

Published on 14 Apr 2026 - 9:55

398

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Complex potential between axes & hyperbola

Published on 10 Apr 2026 - 22:18

138

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Newtonian potential of torus

Published on 10 Apr 2026 - 19:18

156

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Newtonian potential for ellipsoid

Published on 08 Apr 2026 - 17:20

62

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Is the potential of a periodic conservative field periodic?

Published on 11 Apr 2026 - 1:24

171

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The existence of a measure of finite energy implies a lower bound on Hausdorff dimension

Published on 25 Mar 2026 - 17:21

1.1k

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Harmonic functions in the upper half plane

Published on 15 Apr 2026 - 18:20

256

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maps that preserve harmonic functions

Published on 13 Apr 2026 - 18:38

254

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How to finish the computation of $u(x)=\int_{B_R(0)}\frac{1}{|y-x|}dy$?

Published on 16 Apr 2026 - 14:09

2.5k

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You can't solve Laplace's equation with boundary conditions on isolated points. But why?

Published on 12 Apr 2026 - 12:03

212

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A polynomial can be written as the difference of sub-harmonic functions

Published on 13 Apr 2026 - 16:40

63

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Potentials and Markov Processes

Published on 15 Apr 2026 - 11:03

List Question

Riesz measure associated with a subharmonic function

Why is the integral of $\|\nabla f\|^2$ called the energy of $f$?

Finding the transfinite diameter of the level sets of complex logarithm

Show that requiring Electrostatic potential to be a stationary point of Electrostatic potential energy is equivalent to Laplace's equation.

Complex potential between axes & hyperbola

Newtonian potential of torus

Newtonian potential for ellipsoid

Is the potential of a periodic conservative field periodic?

The existence of a measure of finite energy implies a lower bound on Hausdorff dimension

Harmonic functions in the upper half plane

maps that preserve harmonic functions

How to finish the computation of $u(x)=\int_{B_R(0)}\frac{1}{|y-x|}dy$?

You can't solve Laplace's equation with boundary conditions on isolated points. But why?

A polynomial can be written as the difference of sub-harmonic functions

Potentials and Markov Processes

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