The oblique derivative problem for general elliptic systems in Lipschitz domains

The main result of this chapter is a theorem, which addresses the solvability of the oblique derivative problem for general second-order strongly elliptic PDEs in Lipschitz domains. Our arguments, building on an earlier idea of Calderón, make essential use of the results devised earlier. This approach is constructive, in the sense that it relies on integral equation methods; indeed, we prove global representation formulas for the solutions in terms of boundary layer potentials. The trend of using such layer potentials “for general elliptic systems” in the nonsmooth context was suggested by A. P. Calderón.