Last Updated：2025/11/20

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(mathematics, physics) 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.

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Laplace operator

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Source Word

Laplace operator

Noun

Japanese Meaning

数学や物理学において用いられる微分作用素。ℝⁿ上で定義され、記号∆で表され、各変数に対する二階微分を足し合わせた形（∑(∂²/∂x_i²)）を持ち、波動伝播や熱伝導などの現象の解析に利用される。

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The Laplace operator plays a central role in solving the heat equation on Euclidean domains.

Google Translation / DeepL Translation

ラプラシアンはユークリッド領域における熱方程式を解く際に中心的な役割を果たす。

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Sense（1）

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).

Google Translation / DeepL Translation

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Laplace operators

（ plural ）

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Laplace operator

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Laplace operator

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