A secondorder Partial Differential Equation, i.e., one of the form

(1) 
is called elliptic if the Matrix

(2) 
is Positive Definite. Laplace's Equation and Poisson's Equation are examples
of elliptic partial differential equations. For an elliptic partial differential equation, Boundary Conditions are used
to give the constraint
on
, where

(3) 
holds in .
See also Hyperbolic Partial Differential Equation, Parabolic Partial Differential Equation,
Partial Differential Equation
© 19969 Eric W. Weisstein
19990525