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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.
Definition source: English Wiktionary via Wiktextract
Qualifier: potential theory
Examples
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
No etymology was provided for this word.
Across languages
Translations
7 source translations are retained for this English entry.
-
Bulgarian:
уравнение на Лаплас
(uravnenie na Laplas)
— PDE
-
Finnish:
Laplacen yhtälö
— PDE
-
French:
équation de Laplace
— PDE
-
German:
Laplace-Gleichung
— PDE
-
Hungarian:
Laplace-egyenlet
— PDE
-
Polish:
równanie różniczkowe Laplace'a
— PDE
-
Russian:
уравне́ние Лапла́са
(uravnénije Laplása)
— PDE
