Laplace's equation

Noun

(mathematics, physics, 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.

Japanese Meaning

ラプラスの方程式は、数学、物理学、ポテンシャル理論などで用いられる偏微分方程式で、対象となるスカラー関数に対して各座標の二次の偏微分の総和（ラプラス演算子を用いる）が0となる式（𝛥𝜑=0または∇²𝜑=0）として表現される。

What is this buttons?

Laplace's equation governs the behavior of the electrostatic potential in regions without charge.

Google Translation / DeepL Translation

偏微分方程式 ∇²φ = 0（ラプラス方程式）は、電荷のない領域における静電ポテンシャルの振る舞いを支配する。

Details

Sense（1）

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.

Google Translation / DeepL Translation

Details

Laplace's equations

（ plural ）

Details

Laplace's equation

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