Dictionary

Laplace's equation en · NOUN

Meanings

1. (qualifier: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.
   • 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:
   • 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:
   • 2002, Gerald D. Mahan, Applied Mathematics, Kluwer Academic / Plenum, page 141, Laplace's equation appears in a variety of physics problems and several examples are provided below. The relevance of Laplace's equation to complex variables is provided by the following important theorem.

Forms

Translations (7)

hu Laplace-egyenlet (PDE) · fi Laplacen yhtälö (PDE) · fr équation de Laplace (PDE) · de Laplace-Gleichung (PDE) · bg уравнение на Лаплас (PDE) · pl równanie różniczkowe Laplace'a (PDE) · ru уравне́ние Лапла́са (PDE)