Phrase guide

Laplace operator

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

A differential operator, denoted ∆ and defined on Rn as Δ=∑i=1n(∂2)/(∂x_i2), used in the modeling of wave propagation, heat flow and many other applications.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, natural-sciences, physical-sciences, physics, sciences

Examples

  • 1975, Various translators, V. Ja. Sikjrjavyĭ, A Quasidifferentiation Operator and Boundary Value Problems Connected With It, V. I. Averbvh, M. S. Birman, A. A. Blahin (editors), Transactions of the Moscow Mathematical Society for the Year 1972, Volume 27, [ТРУДЫ МОСКОВКОГО МАТЕМАҬИЧЕСКОГО ОБЩЕСТВА ТОМ 27 (1972)], American Mathematical Society, page 202, The first notion of a Laplace operator for functionals on a Hilbert space was introduced by Levy in [l], and the idea was developed further in [2]. Levy's results depended on the posthumous work of Gateaux [3] in which the Dirichlet problem in Hilbert space was considered (without any concise definition of the Laplace operator).

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

21 source translations are retained for this English entry.

  • Bulgarian: оператор на Лаплас (operator na Laplas) — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Chinese Mandarin: 拉普拉斯算子 (Lāpǔlāsī suànzǐ) — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Chinese Mandarin: 調和算子 /调和算子 (tiáohé suànzǐ) — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Estonian: Laplace'i operaator — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Finnish: Laplacen operaattori — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • French: opérateur laplacien — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • German: Laplace-Operator — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Hebrew: לפלסיאן (laplasián) — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Icelandic: Laplace-virki — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Korean: 라플라스 작용소 (Rapeullaseu jagyongso) — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Persian: عملگر لاپلاس ('amalgar-e lâplâs) — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Persian: لاپلاسین (lâplâsiyan) — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Persian: لاپلاسی (lâplâsi) — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Polish: laplasjan — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Portuguese: laplaciano — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Russian: лапласиа́н (laplasián) — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Russian: опера́тор Лапла́са (operátor Laplása) — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Spanish: operador de Laplace — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Spanish: laplaciano — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Swedish: Laplaceoperator — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications
  • Swedish: Laplacian — mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications