The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz

Abstract EN

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 R m ( m ≥ 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.