List questions from potential-theory

Published on 27 Mar 2026 - 3:49

71

Views

Newtonian capacity: do we have $\operatorname{cap}(A\cup B)+\operatorname{cap}(A\cup C)-\operatorname{cap}(A)-\operatorname{cap}(A\cup B\cup C)>0$

Published on 30 Dec 2014 - 3:26

98

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Does small capacity of a set imply that its measure is small too?

Published on 06 Oct 2019 - 6:02

104

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Sets of harmonic measure zero

Published on 18 Oct 2019 - 7:05

44

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Regular set for a nearly Borel set is Borel (Brownian motion)?

Published on 18 Nov 2019 - 18:38

269

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Triple integral for electrostatic potential of a particle in a cubic quantum box

Published on 26 Mar 2026 - 22:14

388

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How to find the vector potential of the field $F = (-y,x,0)$?

Published on 26 Mar 2026 - 16:56

62

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If $F(x + iy) = \frac{Q}{2\pi}\ln (x + iy)$, how to prove that $\phi(x,y) = \frac{Q}{2\pi}\ln (\sqrt{x^2 + y^2})$?

Published on 27 Mar 2026 - 10:12

29

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Far field asymptotic behavior for Strongly Localized Perturbed domain

Published on 26 Mar 2026 - 12:58

153

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For $h,k$ harmonic prove that $hk$ is harmonic if and only if $h +ick$ is holomorphic.

Published on 28 Mar 2026 - 3:27

99

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Solenoidal and irrotational field

Published on 29 Mar 2020 - 22:36

102

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Why is the $1/r^2$ factor retained in Laplace's equation in spherical coordinates?

Published on 25 Mar 2026 - 20:42

122

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Green's Function for the potential

Published on 26 Mar 2026 - 9:44

73

Views

Is there characterization of critical points of the electric potential function?

Published on 09 Apr 2020 - 18:32

39

Views

estimate for exterior harmonic function

Published on 01 May 2020 - 10:27

List Question

$L^2$ regularity of a convolution with Newtonian potential

Newtonian capacity: do we have $\operatorname{cap}(A\cup B)+\operatorname{cap}(A\cup C)-\operatorname{cap}(A)-\operatorname{cap}(A\cup B\cup C)>0$

Does small capacity of a set imply that its measure is small too?

Sets of harmonic measure zero

Regular set for a nearly Borel set is Borel (Brownian motion)?

Triple integral for electrostatic potential of a particle in a cubic quantum box

How to find the vector potential of the field $F = (-y,x,0)$?

If $F(x + iy) = \frac{Q}{2\pi}\ln (x + iy)$, how to prove that $\phi(x,y) = \frac{Q}{2\pi}\ln (\sqrt{x^2 + y^2})$?

Far field asymptotic behavior for Strongly Localized Perturbed domain

For $h,k$ harmonic prove that $hk$ is harmonic if and only if $h +ick$ is holomorphic.

Solenoidal and irrotational field

Why is the $1/r^2$ factor retained in Laplace's equation in spherical coordinates?

Green's Function for the potential

Is there characterization of critical points of the electric potential function?

estimate for exterior harmonic function

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