List questions from harmonic-functions

Published on 18 Apr 2020 - 18:15

805

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A continuous function for which Poisson's equation has no C^2 solutions

Published on 26 Mar 2026 - 1:01

72

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Why is it in $C_c^\infty(\mathbb{R}^n)$?

Published on 19 Apr 2020 - 10:32

61

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Why is $\nabla u (r\cdot 0) = r\nabla u (0)$ true for a harmonic function $u$?

Published on 20 Apr 2020 - 0:10

381

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Dirichlet problem for Laplace equation with square domain

Published on 20 Apr 2020 - 4:15

613

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Subharmonic functions and monotonically increasing integrals

Published on 20 Apr 2020 - 8:45

244

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Harnack's inequality for gradient

Published on 21 Apr 2020 - 15:05

279

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Counter-example to requiring $\Omega$ to be simply connected for existence of harmonic conjugate

Published on 22 Apr 2020 - 5:29

154

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Analytic continuation of $H_x^{(k)}=\sum_{n=1}^x \frac{1}{n^k}$?

Published on 25 Mar 2026 - 11:04

174

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Laplace's equation on Lorentzian manifold

Published on 26 Mar 2026 - 1:02

401

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Proving a harmonic polynomial in $x$ and $y$ is a linear combination of $\Re(x+\mathrm iy)^n$ and $\Im(x+\mathrm iy)^n$

Published on 25 Mar 2026 - 17:42

255

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Why is the p-Laplace Equation quasi-linear?

Published on 27 Apr 2020 - 14:04

456

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dimension of a vector space of harmonic functions among polynomials in two variables

Published on 27 Apr 2020 - 19:15

338

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Prove that $v(x)=\frac{1}{|x|^{n-2}}u(\frac{x}{|x|^2})$ is harmonic

Published on 28 Apr 2020 - 5:47

52

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Construction of purely radial harmonic function

Published on 27 Mar 2026 - 5:37

List Question

Why is $\int_{-\infty}^\infty |\text{sinc}(t)|\ dt=\infty$?

A continuous function for which Poisson's equation has no C^2 solutions

Why is it in $C_c^\infty(\mathbb{R}^n)$?

Why is $\nabla u (r\cdot 0) = r\nabla u (0)$ true for a harmonic function $u$?

Dirichlet problem for Laplace equation with square domain

Subharmonic functions and monotonically increasing integrals

Harnack's inequality for gradient

Counter-example to requiring $\Omega$ to be simply connected for existence of harmonic conjugate

Analytic continuation of $H_x^{(k)}=\sum_{n=1}^x \frac{1}{n^k}$?

Laplace's equation on Lorentzian manifold

Proving a harmonic polynomial in $x$ and $y$ is a linear combination of $\Re(x+\mathrm iy)^n$ and $\Im(x+\mathrm iy)^n$

Why is the p-Laplace Equation quasi-linear?

dimension of a vector space of harmonic functions among polynomials in two variables

Prove that $v(x)=\frac{1}{|x|^{n-2}}u(\frac{x}{|x|^2})$ is harmonic

Construction of purely radial harmonic function

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