The Dirichlet problem for second-order divergence form elliptic operators with variable coefficients: the simple layer potential ansatz (Q304928)

Summary: We investigate the Dirichlet problem related to linear elliptic second-order partial differential operators with smooth coefficients in divergence form in bounded connected domains of \(\mathbb{R}^m\) (\(m \geq 3\)) with Lyapunov boundary. In particular, we show how to represent the solution in terms of a simple layer potential. We use an indirect boundary integral method hinging on the theory of reducible operators and the theory of differential forms.