In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean...

In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete...

In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean...

tensors of rank 0), the connection Laplacian is often called the Laplace–Beltrami operator. It is defined as the trace of the second covariant derivative:...

partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that...

mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation: ∇ 2...

The discrete Laplace operator Δ h u {\displaystyle \Delta _{h}u} depends on the dimension n {\displaystyle n} . In 1D the Laplace operator is approximated...

Kato's inequality is a distributional inequality for the Laplace operator or certain elliptic operators. It was proven in 1972 by the Japanese mathematician...

p-Laplace operator, is a quasilinear elliptic partial differential operator of 2nd order. It is a nonlinear generalization of the Laplace operator, where...

Named after Pierre-Simon Laplace, the graph Laplacian matrix can be viewed as a matrix form of the negative discrete Laplace operator on a graph approximating...

=\nabla \cdot \nabla =\nabla ^{2}} is the Laplace operator, ∇ ⋅ {\displaystyle \nabla \cdot } is the divergence operator (also symbolized "div"), ∇ {\displaystyle...

discrete operators on graphs which are analogous to differential operators in calculus, such as graph Laplacians (or discrete Laplace operators) as discrete...

the Green's function (or fundamental solution) for the Laplacian (or Laplace operator) in three variables is used to describe the response of a particular...

Feature extraction Discrete Laplace operator Prewitt operator Irwin Sobel, 2014, History and Definition of the Sobel Operator K. Engel (2006). Real-time...

Pierre-Simon, Marquis de Laplace (/ləˈplɑːs/; French: [pjɛʁ simɔ̃ laplas]; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has...

In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable...

Inequality. (See talk on the article). As a simple example, consider the Laplace operator Δ. More specifically, suppose that one wishes to solve, for f ∈ L2(Ω)...

sometimes quabla operator (cf. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist...

, {\displaystyle \Delta _{0}\log f=-Kf^{2},} where ∆0 is the flat Laplace operator Δ 0 = ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 = 4 ∂ ∂ z ∂ ∂ z ¯ . {\displaystyle \Delta...

of V, then D is called a Dirac operator. Note that there are two different conventions as to how the Laplace operator is defined: the "analytic" Laplacian...

operator component-wise to each component of the vector. The Laplace operator is a scalar operator that can be applied to either vector or scalar fields; for...

to define discrete Lie derivative on general polygonal meshes . The Laplace operator Δ f {\displaystyle \Delta f} of a function f {\displaystyle f} at a...

\nabla ^{4}} , which is the fourth power of the del operator and the square of the Laplacian operator ∇ 2 {\displaystyle \nabla ^{2}} (or Δ {\displaystyle...

differential equation. In applications to the physical sciences, operators such as the Laplace operator play a major role in setting up and solving partial differential...

be realized as the codifferential opposite to the gradient operator, and the Laplace operator on a function is the divergence of its gradient. An important...

figure, imshow(output_image); title('Edge Detected Image'); Sobel operator Laplace operator Roberts Cross Edge detection Feature detection (computer vision)...

\nabla ^{2}} . In three dimensions using Cartesian coordinates the Laplace operator is ∇ 2 = ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 + ∂ 2 ∂ z 2 {\displaystyle \nabla ^{2}={\frac...

mathematics, the fractional Laplacian is an operator that generalizes the notion of the Laplace operator to fractional powers of spatial derivatives....

Del squared may refer to: Laplace operator, a differential operator often denoted by the symbol ∇2 Hessian matrix, sometimes denoted by ∇2 Aitken's delta-squared...

bounded. This operator is in fact a compact operator. The compact operators form an important class of bounded operators. The Laplace operator Δ : H 2 ( R...