New posts in Laplacian

Proof that $a\nabla^2 u = bu$ is the only homogenous second order 2D PDE unchanged/invariant by rotation

Laplacian of $1/r$ in a tensor

How to shorten the derivation of the Laplacian in polar coordinates?

"Inverse" Helmholtz Decomposition

Proving that the eigenfunctions of the Laplacian form a basis of $L^2(\Omega)$ (and of $H_0^1(\Omega)$)

Dirac's delta in 3 dimensions: proof of $\nabla^2(\|\boldsymbol{x}-\boldsymbol{x}_0\|^{-1})=-4\pi\delta(\boldsymbol{x}-\boldsymbol{x}_0)$

General solution to Laplace Equation

Fundamental solution to the Poisson equation by Fourier transform

Neumann problem for Laplace equation on Balls by using Green function

Resource for learning about the Laplacian on Riemannian manifolds