Word.ws English Dictionary

Laplace's equation

Laplace's equation noun: the partial differential equation (∂²φ)/(∂x_1²)+(∂²φ)/(∂x_2²)+⋯+(∂²φ)/(∂x_n²)=0, commonly written Δφ=0 or ∇²φ=0, where Δ(=∇²) is the Laplace operator and φ is a scalar function.

Noun

Laplace's equation (plural Laplace's equations)

  1. (potential theory) The partial differential equation (∂²φ)/(∂x_1²)+(∂²φ)/(∂x_2²)+⋯+(∂²φ)/(∂x_n²)=0, commonly written Δφ=0 or ∇²φ=0, where Δ(=∇²) is the Laplace operator and φ is a scalar function.
    • In practical problems, since the charges are confined to small regions while major part of the space is charge-free, it is obvious that Laplace's Equation has far greater utility than Poisson's equation.1993, V. V. Sarwate, Electromagnetic Fields and Waves, New Age International Publishers, page 182
    • Numerous problems in electrical engineering require a solution of Laplace's equation in two dimensions. This section outlines a classic problem that leads to Laplace's equation, then develops a finite element method for its solution.1996, Peter P. Silvester, Ronald L. Ferrari, Finite elements for electrical engineers, 3rd edition, Cambridge University Press, page 29

Forms of Laplace's equation

pluralLaplace's equations
alternative formLaplace equation

Questions about Laplace's equation

What does Laplace's equation mean?
Laplace's equation means the partial differential equation (∂²φ)/(∂x_1²)+(∂²φ)/(∂x_2²)+⋯+(∂²φ)/(∂x_n²)=0, commonly written Δφ=0 or ∇²φ=0, where Δ(=∇²) is the Laplace operator and φ is a scalar function.
What part of speech is Laplace's equation?
Laplace's equation is a noun.
What is the plural of Laplace's equation?
The plural of Laplace's equation is Laplace's equations.

Words near Laplace's equation in the dictionary

  1. Laplace sphere
  2. Laplace spheres
  3. Laplace transform
  4. Laplace transforms
  5. Laplace's demon
  6. Laplace's equation
  7. Laplace-Beltrami operator
  8. Laplace-Beltrami operators
  9. Laplace-de Rham operator
  10. Laplacean
  11. Laplaceans

Source and license

Adapted from Wiktionary: Laplace's equation (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “Laplace's equation.” Word.ws, https://word.ws/laplace%27s_equation. Based on Wiktionary, CC BY-SA 4.0.