Earnshaw's theorem relies on this mathematician's statement that the electric force from a potential will always be divergenceless; that version of this man's namesake equation is satisfied by harmonic functions.
This mathematician's namesake operator generalizes to one named for him and Beltrami that is equal to the trace of the Hessian on a Riemannian manifold. Earnshaw's theorem relies on this mathematician's statement that the electric force from a potential will always be divergenceless; that version of this man's namesake equation is satisfied by harmonic functions. This man, whose namesake equation is a special case of the (*) Poisson equation, is the namesake of an integral process that is used to turn differential equations into algebraic equations. The divergence of the gradient of a function is equal to this man's operator often symbolized with an inverted triangle and a 2 in the superscript. For 10 points, name this French mathematician names the del-squared operator.
This mathematician's namesake operator generalizes to one named for him and Beltrami that is equal to the trace of the Hessian on a Riemannian manifold.
Pierre-Simon Laplace 