Question

How to transform area integral $\int_{D} \omega^2 \ dx \ dy$ into boundary integral $\oint_{C} \square \ ds$?

score 45 · Answer 1 · 2026-03-25 23:16:34

45

Views

How to transform area integral $\int_{D} \omega^2 \ dx \ dy$ into boundary integral $\oint_{C} \square \ ds$?

Published on 25 Mar 2026 - 23:16

score 87 · Answer 2 · 2026-03-28 12:13:32

87

Views

Find a and b so that a function is harmonic

Published on 28 Mar 2026 - 12:13

score 40 · Answer 3 · 2023-11-16 23:43:41

40

Views

Question about Evans's proof of of the mean value forlmula for harmonic functions in Partial Differential Equations

Published on 16 Nov 2023 - 23:43

score 21 · Answer 4 · 2026-03-26 14:43:19

21

Views

Solve Poisson problem $ \Delta u(\rho,\phi)=\ln \rho+2\cos^2\phi$ on annulus $1<\rho<3.$

Published on 26 Mar 2026 - 14:43

score 103 · Answer 5 · 2026-03-28 12:02:22

103

Views

$-\log\delta_{\Omega}$ is plurisubharmonic.

Published on 28 Mar 2026 - 12:02

score 29 · Answer 6 · 2023-11-23 20:33:38

29

Views

How to write the general solution to the laplace or helmholtz equation in 3D cylindrical coordinates

Published on 23 Nov 2023 - 20:33

score 36 · Answer 7 · 2023-11-26 03:25:55

36

Views

Extending harmonic function to a codimension 2 subset.

Published on 26 Nov 2023 - 3:25

score 53 · Answer 8 · 2023-11-26 09:41:15

53

Views

If $u\in W^{1,p}(\mathbb{R}^n) \cap C^1{(\mathbb{R}^n)}$ may I suppose that $|u(x)|=\frac{1}{\omega_n} \int_{B_{1}(x)}|u(x)|dy?$ How to prove it?

Published on 26 Nov 2023 - 9:41

score 72 · Answer 9 · 2026-03-28 06:00:31

72

Views

How to calculate the limits of the integral and the outward vector? How to make change of variables in this proof?

Published on 28 Mar 2026 - 6:00

score 76 · Answer 10 · 2026-03-26 14:34:33

76

Views

Prove that $u = |\nabla v|^2$ reaches its maximum in $\partial \Omega$, $v$ being a solution to the given Poisson pde

Published on 26 Mar 2026 - 14:34

score 116 · Answer 11 · 2023-12-01 09:32:36

116

Views

On the solution I got from 2D Laplace equation

Published on 01 Dec 2023 - 9:32

score 74 · Answer 12 · 2026-03-27 00:02:24

74

Views

Solving a Laplace Equation on a Semi infinite Strip

Published on 27 Mar 2026 - 0:02

score 57 · Answer 13 · 2026-03-26 06:20:08

57

Views

Questions about harmonic functions on Cayley graphs

Published on 26 Mar 2026 - 6:20

score 25 · Answer 14 · 2026-03-28 22:26:35

25

Views

Electrostatic potential due to repeating coplanar charged strips (Mathews&Walker 5.1)

Published on 28 Mar 2026 - 22:26

score 23 · Answer 15 · 2026-03-26 21:26:06

23

Views

How to find numerically $\int_{0}^{1} w \langle \mathbf{p}, \mathbf{p}'\rangle \ du$ such $\nabla^2 w=0$ without solving the PDE for $w$ first?

Published on 26 Mar 2026 - 21:26

List Question

How to transform area integral $\int_{D} \omega^2 \ dx \ dy$ into boundary integral $\oint_{C} \square \ ds$?

Find a and b so that a function is harmonic

Question about Evans's proof of of the mean value forlmula for harmonic functions in Partial Differential Equations

Solve Poisson problem $ \Delta u(\rho,\phi)=\ln \rho+2\cos^2\phi$ on annulus $1<\rho<3.$

$-\log\delta_{\Omega}$ is plurisubharmonic.

How to write the general solution to the laplace or helmholtz equation in 3D cylindrical coordinates

Extending harmonic function to a codimension 2 subset.

If $u\in W^{1,p}(\mathbb{R}^n) \cap C^1{(\mathbb{R}^n)}$ may I suppose that $|u(x)|=\frac{1}{\omega_n} \int_{B_{1}(x)}|u(x)|dy?$ How to prove it?

How to calculate the limits of the integral and the outward vector? How to make change of variables in this proof?

Prove that $u = |\nabla v|^2$ reaches its maximum in $\partial \Omega$, $v$ being a solution to the given Poisson pde

On the solution I got from 2D Laplace equation

Solving a Laplace Equation on a Semi infinite Strip

Questions about harmonic functions on Cayley graphs

Electrostatic potential due to repeating coplanar charged strips (Mathews&Walker 5.1)

How to find numerically $\int_{0}^{1} w \langle \mathbf{p}, \mathbf{p}'\rangle \ du$ such $\nabla^2 w=0$ without solving the PDE for $w$ first?

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