Dictionary

elliptic operator en · NOUN

Etymology

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

Meanings

1. Any of a particular class of second-order linear differential operators.
   • 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.
   • Just as in the usual elliptic theory, in the theory of nonlocal elliptic operators we need not restrict ourselves to individual operators but can also consider families of nonlocal elliptic operators. 2008, Vladimir E. Nazaikinskii, Anton Yu. Savin, Boris Yu. Sternin, Elliptic Theory and Noncommutative Geometry: Nonlocal Elliptic Operators, Springer, page 37:
   • The Dirichlet problem for an elliptic operator was solved in Chap. 10 by morphing a solution of the Dirichlet problem for the Laplacian on a ball into a solution of the Dirichlet problem for an elliptic operator on a ball. 2014, Lester L. Helms, Potential Theory, 2nd edition, Springer, page 412:

Forms

Coordinates

hyperbolic operator · parabolic operator

Hyponyms

Laplace operator (second-order linear differential operator)

Relateds

hypoelliptic operator

wikipedia: elliptic partial differential equation