elliptic operator

Etymology
From its association with a corresponding — a second-order linear partial differential equation with coefficients specified analogously to those of the equation of a conic section that generates an ellipse.

Noun

 * 1)  Any of a particular class of second-order linear differential operators.
 * 2) * 2001, L. Gross, Heat Kernel Analysis on Lie Groups, Laurent Decreusefond, Bernt Øksendal, Ali S. Üstünel (editors), Stochastic Analysis and Related Topics VII: Proceedings of the Seventh Silivri Workshop, Springer-Verlag (Birkhäuser), page 1,
 * The study of second order elliptic operators over some of these infinite dimensional manifolds has been the subject of much work in the past forty years, some of it for the purposes of quantum field theory and some of it for the purposes of stochastic analysis or infinite dimensional differential topology.