elliptic differential equation

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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 formwhereA_ij,B_i,C, andFare suitably differentiable real functions ofx₁,x₂, …,x_n, and there exists at each point (x₁,x₂, …,x_n) a real linear transformation on thex_iwhich reduces the quadratic formto a sum ofnsquares, all of the same sign. Also known as elliptic partial differential equation.

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