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

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.

Keywords

• Asymptotic behaviour of solutions
• elliptic systems
• Dirichlet problem
• measurable coefficients.