List questions from harmonic-functions

Published on 13 Jun 2022 - 16:17

103

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Exercise on elliptic PDE

Published on 02 Apr 2026 - 17:39

77

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Problem with a Sturm-Liuville case

Published on 16 Jun 2022 - 8:45

100

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Follow up on decomposition of vector fields

Published on 26 Mar 2026 - 19:37

160

Views

A version of Phragmen-Lindelof principle from Protter-Weinberger's book

Published on 21 Jun 2022 - 13:40

104

Views

How to find harmonic functions satisfying boundary conditions, in polar coordinates.

Published on 26 Jun 2022 - 16:28

124

Views

Developing a correct Ansatz and solving the Laplace equation on a rectangle

Published on 29 Jun 2022 - 9:30

128

Views

Proof verification for a theorem about a harmonic function on the unit disc

Published on 30 Jun 2022 - 20:04

84

Views

Two different recurrence relations, same solution

Published on 01 Jul 2022 - 14:08

55

Views

Sub- and superharmonic functions

Published on 04 Jul 2022 - 11:16

186

Views

Does the Laplace's equation $\nabla^2 u=0$ could have smooth compact-supported solutions $\in C_c^\infty$? Any example?

Published on 04 Jul 2022 - 20:37

331

Views

Schwarz reflection principle and even extension of harmonic functions

Published on 07 Jul 2022 - 10:49

35

Views

What is the mathematical term for a shape that fits in a specific coordinates (e.g. a rectangle in cartesian)?

Published on 25 Mar 2026 - 17:43

86

Views

Discrepancy: steady state of scaled Brownian motion on sphere is not a harmonic function

Published on 25 Mar 2026 - 13:55

53

Views

Let $A$ be the set of points where the gradient of $u$ vanishes. If $A$ has an accumulation point in $\Omega$, is it true that $u$ is constant?

Published on 01 Apr 2026 - 7:20

List Question

Exercise on harmonic functions

Exercise on elliptic PDE

Problem with a Sturm-Liuville case

Follow up on decomposition of vector fields

A version of Phragmen-Lindelof principle from Protter-Weinberger's book

How to find harmonic functions satisfying boundary conditions, in polar coordinates.

Developing a correct Ansatz and solving the Laplace equation on a rectangle

Proof verification for a theorem about a harmonic function on the unit disc

Two different recurrence relations, same solution

Sub- and superharmonic functions

Does the Laplace's equation $\nabla^2 u=0$ could have smooth compact-supported solutions $\in C_c^\infty$? Any example?

Schwarz reflection principle and even extension of harmonic functions

What is the mathematical term for a shape that fits in a specific coordinates (e.g. a rectangle in cartesian)?

Discrepancy: steady state of scaled Brownian motion on sphere is not a harmonic function

Let $A$ be the set of points where the gradient of $u$ vanishes. If $A$ has an accumulation point in $\Omega$, is it true that $u$ is constant?

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