Two generalizations of its continuous formulation are related by a Weitzenb?ck identity, while the discrete version of this operation evaluated on a graph vertex sums the diff
Two generalizations of its continuous formulation are related by a Weitzenb?ck identity, while the discrete version of this operation evaluated on a graph vertex sums the difference between the function value at that vertex and all of its nearest neighbors. Under conditions of chemical equilibrium, it vanishes when applied to the density of a quantity like concentration, and a generalization of it is found in a relativistic version of the Schr?dinger equation, the Klein-Gordon equation. Earnshaw's theorem invokes it to show that an electrical force derived from a potential function must have zero divergence, and when it is evaluated on Minkowski space, it is called the d'Alembertian. For 10 points, identify this elliptic operator which vanishes for harmonic functions, the divergence of the gradient, named for a Frenchman.
Two generalizations of its continuous formulation are related by a Weitzenb?ck identity, while the discrete version of this operation evaluated on a graph vertex sums the difference between the function value at that vertex and all of its nearest neighbors.
Laplacian [or Laplace operator]