Layer potentials and boundary value problems for elliptic systems in Lipschitz domains (Q810274)

The author studies boundary value problems in Lipschitz domains for general second order linear elliptic systems of partial differential equations with constant coefficients. Suitable layer potential operators are constructed to show the unique solvability of the Dirichlet problem with boundary data in \(L^ p\)(\(\partial \Omega)\) for p close to 2; the method applies to elliptic systems whose coefficients satisfy the Legendre-Hadamard condition and a symmetry condition. The oblique derivative problem is also considered.