(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.

plural of Laplace expansion

(mathematics) An expression for the determinant |B| of an n × n matrix B that is a weighted sum of the determinants of n submatrices (or minors) of B, each of size (n − 1) × (n − 1).

A generalized version of the Laplace operator that can be used with Riemannian and pseudo-Riemannian manifolds.

plural of Laplace-Beltrami operator

(physics) A nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension.

(differential geometry) A generalization of the Laplace operator; the anticommutator of the exterior derivative and the codifferential.