Layer potentials for general linear elliptic systems

Abstract

In this article we construct layer potentials for elliptic differential operators using the Babuska-Lax-Milgram theorem, without recourse to the fundamental solution; this allows layer potentials to be constructed in very general settings. We then generalize several well known properties of layer potentials for harmonic and second order equations, in particular the Green's formula, jump relations, adjoint relations, and Verchota's equivalence between well-posedness of boundary value problems and invertibility of layer potentials.

Keywords

• Higher order differential equation
• layer potentials
• Dirichlet problem
• Neumann problem