The Cauchy Problem for a Second Order Elliptic Equation.
by
Ian Knowles
Univ of Alabama - Birmingham

The Cauchy problem for an elliptic equation is one of the archetypal ill-posed problems discussed by Jacques Hadamard in his lectures given in the early part of the last century. Far from being physically meaningless, as inferred by Hadamard, these problems arise naturally in areas such as electrocardiography, where one is interested in the reconstruction of the epicardial potential from body surface data. We introduce a new method for computing the solution of these Cauchy problems by reformulating to a variational problem involving the minimization of a non-negative functional with a unique global minimum and a unique stationary point.

Date received: May 21, 2002