# Questions tagged [poissons-equation]

In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in electrostatics, mechanical engineering and theoretical physics. (Def: https://en.wikipedia.org/wiki/Poisson%27s_equation)

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### Green’s function of poisson’s equation in general dimensions

Green’s function of the Helmholtz equation, in the general dimension D, can be calculated as follows: \begin{align} G(\mathbf{r})&=\int \frac{d^D{k}}{(2\pi)^D} \frac{e^{-i \mathbf{k}\mathbf{r}}}{\...
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### Poisson equation in a cylinder

I need to solve the problem $\nabla^{2} u(r,\theta,z)=Q(r,\theta,z)$ inside a circular cylinder $(0 < r < a, 0 < \theta < 2\pi, 0 < z < H)$ subject to $u = 0$ on the sides. I'm ...
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### Evaluating limits of the type $\left.[e^{ikx}\Phi(x)]\right|_{x=-\infty}^{x=\infty}$

How to evaluate limits of the type: $$\left.[e^{ikx}\Phi(x)]\right|_{x=-\infty}^{x=\infty}$$ Such terms occur while trying to integrate by parts when taking the Fourier Transform of the Poisson ...