Question

Laplace's equation on hyperbolic disk whose semi circles have different boundary conditions

score 39 · Answer 1 · 2026-03-29 13:23:26

39

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Laplace's equation on hyperbolic disk whose semi circles have different boundary conditions

Published on 29 Mar 2026 - 13:23

score 43 · Answer 2 · 2023-04-26 14:35:41

43

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Prove $\sup_{B_{1/2}(0)} |D^k u| \leq C \| u \|_{L^2(B_1(0))}$, and why do we have $L^2$ norm

Published on 26 Apr 2023 - 14:35

score 128 · Answer 3 · 2026-02-23 03:29:45

128

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How are these two different definitions of the Poisson kernel on the n-torus related?

Published on 23 Feb 2026 - 3:29

score 229 · Answer 4 · 2026-03-25 22:11:00

229

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Why are eigenvectors of Laplace operator commonly used as orthogonal basis?

Published on 25 Mar 2026 - 22:11

score 127 · Answer 5 · 2026-03-27 01:45:00

127

Views

Partial Differential Equation on a Riemannian Manifold: How to solve complex second order ODE by hand.

Published on 27 Mar 2026 - 1:45

score 102 · Answer 6 · 2026-03-26 18:58:43

102

Views

Laplace's equation in cylinder — does a solution exist?

Published on 26 Mar 2026 - 18:58

score 125 · Answer 7 · 2023-05-09 10:18:21

125

Views

Is the value of a harmonic function must be real?

Published on 09 May 2023 - 10:18

score 56 · Answer 8 · 2026-03-25 20:09:52

56

Views

Absorbing constants when determining them through boundary conditions

Published on 25 Mar 2026 - 20:09

score 44 · Answer 9 · 2023-05-09 18:47:09

44

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Finding initial conditions such that the formal solution of Laplace equation doesn't converge

Published on 09 May 2023 - 18:47

score 53 · Answer 10 · 2023-05-10 17:41:16

53

Views

Proving mean value property for two dimensional harmonic functions without Divergence Theorem or complex calculus

Published on 10 May 2023 - 17:41

score 97 · Answer 11 · 2026-03-25 22:30:43

97

Views

Continuity of solutions of Laplace's equation on the unit disk with piecewise $\mathcal{C}^1$ boundary condition

Published on 25 Mar 2026 - 22:30

score 21 · Answer 12 · 2023-05-22 14:26:00

21

Views

Specific proof for Liouville’s theorem for dimension $2$ using Liouville’s theorem from complex analysis

Published on 22 May 2023 - 14:26

score 113 · Answer 13 · 2026-03-26 11:05:30

113

Views

Comparison principle for p-harmonic functions.

Published on 26 Mar 2026 - 11:05

score 280 · Answer 14 · 2026-03-25 19:05:56

280

Views

On the existence of Green's functions by Peter Lax

Published on 25 Mar 2026 - 19:05

score 198 · Answer 15 · 2023-05-27 14:18:10

198

Views

Angular frequency of a coupled oscillator

Published on 27 May 2023 - 14:18

List Question

Laplace's equation on hyperbolic disk whose semi circles have different boundary conditions

Prove $\sup_{B_{1/2}(0)} |D^k u| \leq C \| u \|_{L^2(B_1(0))}$, and why do we have $L^2$ norm

How are these two different definitions of the Poisson kernel on the n-torus related?

Why are eigenvectors of Laplace operator commonly used as orthogonal basis?

Partial Differential Equation on a Riemannian Manifold: How to solve complex second order ODE by hand.

Laplace's equation in cylinder — does a solution exist?

Is the value of a harmonic function must be real?

Absorbing constants when determining them through boundary conditions

Finding initial conditions such that the formal solution of Laplace equation doesn't converge

Proving mean value property for two dimensional harmonic functions without Divergence Theorem or complex calculus

Continuity of solutions of Laplace's equation on the unit disk with piecewise $\mathcal{C}^1$ boundary condition

Specific proof for Liouville’s theorem for dimension $2$ using Liouville’s theorem from complex analysis

Comparison principle for p-harmonic functions.

On the existence of Green's functions by Peter Lax

Angular frequency of a coupled oscillator

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