Electron. J. Diff. Eqns., Vol. 2006(2006), No. 10, pp. 1-46.

Asymptotic representation of solutions to the Dirichlet problem for elliptic systems with discontinuous coefficients near the boundary

Vladimir Kozlov

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.

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Vladimir Kozlov
Department of Mathematics, University of Linköping
SE-581 83 Linköping, Sweden
email: vlkoz@mai.liu.se

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