List questions from harmonic-functions

Published on 25 Mar 2026 - 6:08

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Showing that $u$ is constant if $u$ and $u^2$ are harmonic

Published on 28 Sep 2018 - 7:13

398

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Equivalence of local mean value property and mean value property

Published on 28 Sep 2018 - 21:18

129

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In general, what information is given by $\nabla^2 f \geq 0$?

Published on 03 Oct 2018 - 4:18

173

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PDE Laplace equation Calculate $u(x,0)$.

Published on 03 Oct 2018 - 12:38

75

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What is the closure of $h^2(U)$ in the topology of the uniform convergence on upper half planes?

Published on 25 Mar 2026 - 6:12

121

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Find a harmonic function u that vanishes on C[0, 2] and satisfies $u(3e^{i\theta}) = 65\cos(2\theta)$

Published on 06 Oct 2018 - 18:03

335

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partial differential equations, Laplace equation, boundary conditions

Published on 24 Mar 2026 - 19:48

52

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Considering two regions and a holomorphic function, show the following

Published on 13 Oct 2018 - 18:53

110

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Difference of fundamental solutions

Published on 24 Mar 2026 - 23:43

97

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Surface Integral - Mean Value Property

Published on 15 Oct 2018 - 15:53

106

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Finite invariant measures for reversible Markov chain

Published on 17 Oct 2018 - 10:08

34

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An (sort of) inverse Dirichlet problem

Published on 17 Oct 2018 - 16:44

207

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Find harmonic function vanishing on the boundary and with a specific bound

Published on 25 Mar 2026 - 6:10

435

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Harmonic functions on an irreducible recurrent Markov chain are constant

Published on 19 Oct 2018 - 10:23

List Question

Proof that Poisson formula solves the Neumann Problem for Laplace Equation in Unit Disk

Showing that $u$ is constant if $u$ and $u^2$ are harmonic

Equivalence of local mean value property and mean value property

In general, what information is given by $\nabla^2 f \geq 0$?

PDE Laplace equation Calculate $u(x,0)$.

What is the closure of $h^2(U)$ in the topology of the uniform convergence on upper half planes?

Find a harmonic function u that vanishes on C[0, 2] and satisfies $u(3e^{i\theta}) = 65\cos(2\theta)$

partial differential equations, Laplace equation, boundary conditions

Considering two regions and a holomorphic function, show the following

Difference of fundamental solutions

Surface Integral - Mean Value Property

Finite invariant measures for reversible Markov chain

An (sort of) inverse Dirichlet problem

Find harmonic function vanishing on the boundary and with a specific bound

Harmonic functions on an irreducible recurrent Markov chain are constant

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