|
gptkbp:instanceOf
|
differential operator
|
|
gptkbp:actsOn
|
vector fields
scalar fields
|
|
gptkbp:alsoKnownAs
|
gptkb:Laplacian
|
|
gptkbp:application
|
fluid dynamics
quantum mechanics
image processing
potential theory
harmonic functions
electrostatics
|
|
gptkbp:category
|
mathematical physics
partial differential equations
vector calculus
|
|
gptkbp:defines
|
sum of all unmixed second partial derivatives of a function
|
|
gptkbp:dimensions
|
defined in any number of dimensions
|
|
gptkbp:eigenfunctions
|
spherical harmonics
Fourier modes
|
|
gptkbp:expressionInCartesianCoordinates
|
∇²f = ∂²f/∂x² + ∂²f/∂y² + ∂²f/∂z²
|
|
gptkbp:field
|
gptkb:mathematics
engineering
physics
|
|
gptkbp:generalizes
|
gptkb:d'Alembert_operator
gptkb:Laplace–Beltrami_operator
|
|
gptkbp:hasInvariant
|
gptkb:Euclidean_transformations
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Laplace operator
|
|
gptkbp:inComplexAnalysis
|
related to Cauchy–Riemann equations
|
|
gptkbp:inQuantumMechanics
|
kinetic energy term in Schrödinger equation
|
|
gptkbp:inRiemannianGeometry
|
gptkb:Laplace–Beltrami_operator
|
|
gptkbp:namedAfter
|
gptkb:Pierre-Simon_Laplace
|
|
gptkbp:notation
|
div grad
Δ
∇²
|
|
gptkbp:property
|
elliptic operator
invariant under rotations
self-adjoint
|
|
gptkbp:relatedTo
|
gptkb:Green's_identities
harmonic analysis
spectral theory
curl
divergence
gradient
|
|
gptkbp:symbol
|
∇²
|
|
gptkbp:type
|
linear operator
second-order operator
|
|
gptkbp:usedIn
|
gptkb:heat_equation
gptkb:wave_equation
gptkb:Schrödinger_equation
gptkb:Laplace's_equation
gptkb:Poisson's_equation
|
|
gptkbp:bfsParent
|
gptkb:Pierre-Simon_Laplace
|
|
gptkbp:bfsLayer
|
5
|