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

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

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:...

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

\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...

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

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...

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

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...

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

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...

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

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

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...

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...

, {\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...

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

an operator that takes scalar to a scalar. It can be extended to operate on a vector, by separately operating on each of its components. The Laplace operator...

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...

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

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...

corresponding multiplication is graded-commutative. See references. The Laplace operator Δ f {\displaystyle \Delta f} of a function f {\displaystyle f} at a...

Ja. (1980), "The second term of the spectral asymptotics for a Laplace–Beltrami operator on manifolds with boundary", Funktsional. Anal. I Prilozhen, 14...

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

{L}}\{f(t)\}+b{\mathcal {L}}\{g(t)\}} and is, therefore, regarded as a linear operator. The Laplace transform of f ( t − a ) u ( t − a ) {\displaystyle f(t-a)u(t-a)}...

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...

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)...