It is equivalent to the trace of the Hessian matrix of a function and in Minkowski spacetime and the d'Alembertian operator is an application of it. It can also be applied, component-wise, to vector fields, in which case in three dimensions it is equal to the gradient of the divergence minus the curl of the curl. The problem of finding an unknown function from the result of this operator applied to the function is known as Poisson's equation. This linear second-order differential operator also appears in electrostatics where it relates the potential to the charge densi
It is equivalent to the trace of the Hessian matrix of a function and in Minkowski spacetime and the d'Alembertian operator is an application of it. It can also be applied, component-wise, to vector fields, in which case in three dimensions it is equal to the gradient of the divergence minus the curl of the curl. The problem of finding an unknown function from the result of this operator applied to the function is known as Poisson's equation. This linear second-order differential operator also appears in electrostatics where it relates the potential to the charge density. Functions for which this is zero everywhere are called harmonic functions and have no local extrema, and their average value over a spherical surface is equal to their value at the center of that sphere. For 10 points, name this scalar operator equal to the divergence of the gradient.
It is equivalent to the trace of the Hessian matrix of a function and in Minkowski spacetime and the d'Alembertian operator is an application of it.
{Laplace} operator or {Laplacian}