Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 106, pp. 1-10.

Title: Modified quasi-boundary value method for Cauchy problems
       of elliptic equations with variable coefficients
       
Author: Hongwu Zhang (Lanzhou Univ., Gansu, China)

Abstract:
 In this article, we study a Cauchy problem for an elliptic
 equation with variable coefficients.  It is well-known that such a
 problem is severely ill-posed; i.e., the solution does not depend
 continuously on the Cauchy data. We propose a modified quasi-boundary
 value regularization method to solve it. Convergence estimates are
 established under two a priori assumptions on the exact solution.
 A numerical example is given to illustrate our proposed method.

Submitted May 4, 2011. Published August 23, 2011.
Math Subject Classifications: 35J15, 35J57, 65G20, 65T50.
Key Words: Ill-posed problem; Cauchy problem; elliptic equation;
           quasi-boundary value method; convergence estimates.