# elliptic differential equation

## elliptic differential equation

[ə′lip·tik dif·ə¦ren·chəl i′kwā·zhən] (mathematics)

A general type of second-order partial differential equation which includes Laplace's equation and has the form where

*A*_{ij },*B*_{i },*C*, and*F*are suitably differentiable real functions of*x*_{1},*x*_{2}, …,*x*_{n }, and there exists at each point (*x*_{1},*x*_{2}, …,*x*_{n }) a real linear transformation on the*x*_{i }which reduces the quadratic form to a sum of*n*squares, all of the same sign. Also known as elliptic partial differential equation.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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