Poisson equation

Poisson方程

Analysis, Measure & PDE · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

The Poisson equation is an inhomogeneous Laplace equation -Delta u=f on an open set, with prescribed source f; using Delta u=f instead changes the sign convention for the source.

Poisson 方程是带给定源项的非齐次 Laplace 方程，此处约定 -Δu=f；若采用 Δu=f，则右端符号相应改变。

Example

In Rn\mathbb R^n, u(x)=−∣x∣2/(2n)u(x)=-|x|^2/(2n) satisfies −Δu=1-\Delta u=1.

Usage and distinctions

Poisson equation names a PDE; Poisson distribution names a probability law and is a separate sense.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. John K. Hunter — Notes on Partial Differential EquationsChapter 2 opening, Poisson equation; §4.1, equation (4.1) · Checked 2026-10-14

Translation sources

  1. 孙天阳 — 偏微分方程2§1.7 Dirichlet边值的Poisson方程经典解的存在性，printed p.17 · Checked 2026-10-14
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