elliptic differential equation
elliptic differential equation[ə′lip·tik dif·ə¦ren·chəl i′kwā·zhən]
A general type of second-order partial differential equation which includes Laplace's equation and has the form where Aij , Bi , C, and F are suitably differentiable real functions of x1, x2, …, xn , and there exists at each point (x1, x2, …, xn ) a real linear transformation on the xi 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.