Laplacian

Japanese: Laplacian

…In this case, for a function u ( x ) that is twice continuously differentiable in Ω, A is a differential operator, also called a partial differential operator in this case. Partial differential operators are particularly important, and are called the Laplacian or Laplace operator. In functional analysis, we define the function space to be considered, and treat the differential operator as a mapping from one function space to another. …

From [Partial Differential Equations]

…Second-order partial differential equations appear in mathematical physics problems such as the following. For a function u ( x ) of a point x = ₍ x1 , x2 , ..., xn ) in space, we define the partial differential operator Δ, called the Laplacian, _as follows: _n is the dimension of the space. …

*Some of the terminology explanations that mention "Laplacian" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…このとき，Ωで2回連続微分可能な関数u(x)に対し，なるAは微分作用素であって，この場合は偏微分作用素とも呼ばれる。とくに偏微分作用素は重要で，ラプラシアンLaplacian，またはラプラス作用素と呼ばれる。関数解析学では，考察する関数空間を定めて，微分作用素を関数空間から関数空間への写像として取り扱う。…