Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 10, pp. 1-46.

Title: Asymptotic representation of solutions to the Dirichlet
       problem for elliptic systems with discontinuous coefficients 
       near the boundary
       
Author: Vladimir Kozlov (Univ. of Linkoping, Sweden)

Abstract: 
 We consider variational solutions to the Dirichlet problem for
 elliptic systems of arbitrary order. It is assumed that  the
 coefficients of the principal part of the system have small, in an
 integral sense, local oscillations near a boundary point and other
 coefficients may have singularities at this point. We obtain an
 asymptotic representation for these solutions and derive sharp
 estimates for them which explicitly contain information on the
 coefficients.
 
Submitted April 24, 2005. Published January 24, 2006.
Math Subject Classifications: 35B40, 35B65, 35J15, 35D10.
Key Words: Asymptotic behaviour of solutions; elliptic systems;
           Dirichlet problem; measurable coefficients.