List questions from laplacian

Published on 26 Mar 2026 - 6:33

158

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What is the historical background of "Hyperbolic Laplacian" $\Delta_{k}=-y^2(\partial^2_{x}+\partial^2_{y})+iky(\partial_{x}+\partial_{y})$?

Published on 28 Mar 2026 - 21:06

1.7k

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Maximum Principle fot the pde : $\Delta u=u^3$

Published on 26 Mar 2026 - 6:32

409

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An MO answer by Terry Tao regarding what the Laplacian measures

Published on 18 Nov 2016 - 15:14

643

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Fractional Laplacian

Published on 27 Mar 2026 - 15:33

106

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Proving properties of Laplacian matrices

Published on 29 Nov 2016 - 15:14

1.1k

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Laplacian in curvilinear coordinates

Published on 29 Nov 2016 - 15:15

119

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Special vector x such that L + xx^T and Cholesky.

Published on 01 Dec 2016 - 10:27

36

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Prove $\Delta(|x|^m)= m(m+n-2)|x|^{m-2}$ pointwise in $\mathbb{R}^n\backslash\{0\}$ for all $ m \in \mathbb{R}$

Published on 04 Dec 2016 - 14:13

1k

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No solution to Laplace equation boundary value problem

Published on 29 Mar 2026 - 12:03

242

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Spectral decomposition of $L^2(\Gamma \setminus \mathbb{H})$

Published on 25 Mar 2026 - 19:03

101

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Example of smallest nonzero eigenvalue of Laplace-Beltrami operator having multiplicity 1.

Published on 08 Dec 2016 - 14:45

206

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Inverting Laplacian on tensor product of Sobolev spaces.

Published on 09 Dec 2016 - 2:22

271

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Contradiction with the boundary condition (at the corner) of Laplace equation

Published on 13 Dec 2016 - 20:56

138

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Rearrangement of Laplacian function

Published on 28 Mar 2026 - 19:28

List Question

Maximum Principle for the PDE $\Delta u=u^2$

What is the historical background of "Hyperbolic Laplacian" $\Delta_{k}=-y^2(\partial^2_{x}+\partial^2_{y})+iky(\partial_{x}+\partial_{y})$?

Maximum Principle fot the pde : $\Delta u=u^3$

An MO answer by Terry Tao regarding what the Laplacian measures

Fractional Laplacian

Proving properties of Laplacian matrices

Laplacian in curvilinear coordinates

Special vector x such that L + xx^T and Cholesky.

Prove $\Delta(|x|^m)= m(m+n-2)|x|^{m-2}$ pointwise in $\mathbb{R}^n\backslash\{0\}$ for all $ m \in \mathbb{R}$

No solution to Laplace equation boundary value problem

Spectral decomposition of $L^2(\Gamma \setminus \mathbb{H})$

Example of smallest nonzero eigenvalue of Laplace-Beltrami operator having multiplicity 1.

Inverting Laplacian on tensor product of Sobolev spaces.

Contradiction with the boundary condition (at the corner) of Laplace equation

Rearrangement of Laplacian function

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