Laplacian vector field (964 bytes)
3: In [[vector calculus]], a '''Laplacian vector field''' is a [[vector field]] which is bo...
13: Therefore, the potential of a Laplacian field satisfies [[Laplace's equation]].

Laplace operator (4233 bytes)
1: ...ctor calculus]], the '''Laplace operator''' or '''Laplacian''' is a [[differential operator]] equal to the su...
10: ...-dimensional [[Cartesian coordinate system]], the Laplacian is:
42: The Laplacian is linear:
50: If you attempt to approximate the Laplacian via numeric methods, you will observe some intere...
56: ...clidean space, one observes that the value of the Laplacian of a function is simply that amount by which the ...

Dirac operator (2403 bytes)
1: ... with [[special relativity]]; to get the relevant Laplacian as a product of first order operators he introduc...
10: <math>\triangle</math> being the Laplacian of <math>V</math>, <math>D</math> is
14: of <math>D^2</math> must equal the Laplacian.

Vector operator (1130 bytes)
8: The [[Laplacian]] is
17: ...vector operator, as seen above in the case of the Laplacian.

Marr-Hildreth algorithm (264 bytes)
1: ...]] in [[digital image]]s. It is also called the [[Laplacian]] of [[Gaussian]]. [[David Marr]] was one of the...

Discrete Laplace operator (3219 bytes)
4: ...ces to [[complex number]]s. Then, the ''discrete Laplacian'' <math>\Delta</math> acting on <math>\phi</math>...
14: ...cian can be shown to correspond to the continuous Laplacian in the limit of an infinitely fine grid. Thus, f...
21: This definition of the Laplacian is commonly used in [[numerical analysis]] and in...

Vector fields in cylindrical and spherical coordinates (6026 bytes)
59: == Gradient, divergence, curl, and laplacian in cylindrical coordinates ==
61: ... of [[gradient]], [[divergence]], [[curl]], and [[laplacian]] in
122: == [[Gradient]], [[divergence]], [[curl]], and [[laplacian]] in spherical coordinates ==
124: ... specification of gradient, divergence, curl, and laplacian in

Elliptic operator (1813 bytes)
2: ...mportant example of an elliptic operator is the [[Laplacian]]. Equations of the form
28: '''Example'''. The negative of the [[Laplacian]] in '''R'''^''n'' given by

Weakly harmonic (505 bytes)
3: ...inuous second derivatives, where &Delta; is the [[Laplacian]]. Surprisingly, this definition is equivalent to...

List of multivariable calculus topics (1509 bytes)
38: *[[Laplacian]]
39: *[[Laplacian vector field]]

Incompressible fluid (2258 bytes)
32: ... the velocity field is actually [[Laplacian field|Laplacian]].

Nabla in cylindrical and spherical coordinates (7198 bytes)
80: <!-- laplacian f -->
90: <!-- laplacian A -->
116: ...cdot (\nabla f) = \nabla^2 f = \Delta f</math> ([[Laplacian]])

Newtonian potential (878 bytes)
1: ...ulus]] that acts as the inverse to the negative [[Laplacian]], on functions that are smooth and decay rapidly...

Hodge theory (2985 bytes)
1: ...l differential equation]] theory of generalised [[Laplacian]] operators associated to a [[Riemannian metric]]...
39: ... de Rham cohomology class picked out by the Hodge Laplacian (generalising [[harmonic function]]s, which must ...
47: ...a more directly algebraic interpretation, without Laplacians, for this case.

Poisson's equation (923 bytes)
17: i.e., it sets the [[Laplace operator|Laplacian]] equal to ''f''.

Neumann boundary condition (906 bytes)
24: ...math>\Delta</math> denotes the [[Laplace operator|laplacian]]), the Neumann boundary condition typically take...

D'Alembert's paradox (7758 bytes)
12: ...an field|Laplacian]]. An object moving through a Laplacian fluid which is at rest (except locally for its di...
14: Perhaps the answer to this paradox is that Laplacian fluids do not really exist in nature: they are a ...
28: ...re one: the definition of D'Alembert's Paradox: ''Laplacian flow produces no drag''.
59: ...ue to the liquid being irrotational and therefore Laplacian. Physically, this is due to the fluid being non-...

Lamellar vector field (986 bytes)
13: ...amellar field which is also [[solenoidal]] is a [[Laplacian field]].

Dirichlet boundary condition (1100 bytes)
24: ...math>\Delta</math> denotes the [[Laplace operator|laplacian]]), the Dirichlet boundary condition typically ta...

Admittance matrix (1120 bytes)
1: ...[graph theory]] the '''admittance matrix''' or '''Laplacian matrix''' is a [[matrix (mathematics)|matrix]] re...

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