List questions from harmonic-functions

Published on 18 May 2019 - 0:20

161

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Understanding proof: if $u: \Omega \subset \mathbb{R}^N \to \mathbb{R}$ is harmonic and $\nabla u \in L^2(\mathbb{R}^N)$, then $u$ is constant.

Published on 18 May 2019 - 15:17

640

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Convergence of harmonic functions in $L^1$ implies uniform convergence on compact sets

Published on 19 May 2019 - 18:52

168

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Perron's Method with Measurable Boundary Data

Published on 26 Mar 2026 - 6:26

478

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Solving Laplace equation with conformal mapping for a region of radius $R$ and angle $\alpha$?

Published on 25 Mar 2026 - 17:22

423

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Confusion about Liouville's theorem for Harmonic functions

Published on 27 May 2019 - 15:35

43

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Sum of two sinusoids in order to write it on new standard form

Published on 30 May 2019 - 13:47

76

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What exactly is going on here? (Trigonometric functions)

Published on 01 Jun 2019 - 12:29

877

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About the sub-mean value property

Published on 01 Jun 2019 - 16:24

61

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show that $u(x) = \frac{1}{2\pi} \int_{R^2} log(|y-x|)\Delta u(y)dy$

Published on 04 Jun 2019 - 0:52

161

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Prove that if $u:\mathbb{R}^d \to \mathbb{R}$ is harmonic with integrable square then $u\equiv 0$.

Published on 04 Jun 2019 - 17:19

126

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Dirichlet problem on a wire: a co-dimension 2 boundary condition

Published on 25 Mar 2026 - 4:38

350

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Uniform convergence of Poisson Kernel (of the upper half plane)

Published on 08 Jun 2019 - 1:51

1.1k

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Bounded Subharmonic functions in the Plane are constant.

Published on 25 Mar 2026 - 21:46

150

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How does this inequality follow?

Published on 25 Mar 2026 - 11:09

List Question

Prove harmonic function inequality with the Mean-Value Property

Understanding proof: if $u: \Omega \subset \mathbb{R}^N \to \mathbb{R}$ is harmonic and $\nabla u \in L^2(\mathbb{R}^N)$, then $u$ is constant.

Convergence of harmonic functions in $L^1$ implies uniform convergence on compact sets

Perron's Method with Measurable Boundary Data

Solving Laplace equation with conformal mapping for a region of radius $R$ and angle $\alpha$?

Confusion about Liouville's theorem for Harmonic functions

Sum of two sinusoids in order to write it on new standard form

What exactly is going on here? (Trigonometric functions)

About the sub-mean value property

show that $u(x) = \frac{1}{2\pi} \int_{R^2} log(|y-x|)\Delta u(y)dy$

Prove that if $u:\mathbb{R}^d \to \mathbb{R}$ is harmonic with integrable square then $u\equiv 0$.

Dirichlet problem on a wire: a co-dimension 2 boundary condition

Uniform convergence of Poisson Kernel (of the upper half plane)

Bounded Subharmonic functions in the Plane are constant.

How does this inequality follow?

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