elliptic operator

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.

Definitions

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

    • 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.

The neighborhood

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA