Meaning of elliptic operator | Babel Free

Definitions

Any of a particular class of second-order linear differential operators.

Examples

“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.”

“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.”

CEFR level