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.