LAYER POTENTIALS AND BOUNDARY-VALUE-PROBLEMS FOR ELLIPTIC-SYSTEMS IN LIPSCHITZ-DOMAINS

Various layer potential operators are constructed for general elliptic systems of partial differential equations with constant coefficients. These operators are used to study the boundary value problems for these systems. For Ω, a bounded Lipschitz domain in Rn, n ≥ 3, it is shown that if the coefficients of the system satisfy the Legendre-Hadamard condition and a symmetry condition, then there exists a unique solution u of the system that solves the Dirichlet problem for given data g in Lp(∂Ω) for p in a neighborhood of 2. Also, the oblique derivative problem for the system is studied. Furthermore, some regularity results for the Dirichlet problem are obtained. © 1991.